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1
REIMER, ANDREW P. "Le je(u) de La mémoire tatouée ." University of Cincinnati / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1132344191.
Повний текст джерела
2
Hertz, Erik. "Parabolic Synthesis." Licentiate thesis, Department of Electrical and Information Technology Faculty of Engineering, LTH, Lund University, Lund, Sweden, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-22338.
Повний текст джерелаАнотація:
Many consumer products, such as within the computer areas, computer graphics, digital signal processing, communication systems, robotics, navigation, astrophysics, fluid physics, etc. are searching for high computational performance as a consequence of increasingly more advanced algorithms in these applications. Until recently the down scaling of the hardware technology has been able to fulfill these higher demands from the more advanced algorithms with higher clock rates on the chips. This that the development of hardware technology performance has stagnated has moved the interest more over to implementation of algorithms in hardware. Especially within wireless communication the desire for higher transmission rates has increased the interest for algorithm implementation methodologies. The scope of this thesis is mainly on the developed methodology of parabolic synthesis. The parabolic synthesis methodology is a methodology for implementing approximations of unary functions in hardware. The methodology is described with the criteria's that have to be fulfilled to perform an approximation on a unary function. The hardware architecture of the methodology is described and to this a special hardware that performs the squaring operation. The outcome of the presented research is a novel methodology for implementing approximations of unary functions such as trigonometric functions, logarithmic functions, as well as square root and division functions etc. The architecture of the processing part automatically gives a high degree of parallelism. The methodology is founded on operations that are simple to implement in hardware such as addition, shifts, multiplication, contributes to that the implementation in hardware is simple to perform. The hardware architecture is characterized by a high degree of parallelism that gives a short critical path and fast computation. The structure of the methodology will also assure an area efficient hardware implementation.
3
Silk, Melissa. "The Possibilities of the Parabola." Thesis, The University of Sydney, 2014. http://hdl.handle.net/2123/13160.
Повний текст джерелаАнотація:
The present study details an investigation into the provision of opportunities for secondary school students to develop an understanding of visual aesthetics by manipulating a single mathematical curve: the parabola. The study documents the establishment of a robust cross-curricular relationship between Mathematics and Visual Design by providing a pedagogical model for learning that relies on the conduit between the two subject areas being explicitly linked. Although the central concept is the marriage of disparate themes, it was operationalised by the development and delivery of activities sequenced to grow appreciation and understanding of the links between unrelated curricula. While this account aims to foster cross-curricular discourse and action, the product output simultaneously provided avenues for the presentation and exhibition of student work; a gallery of which is included in the study. Documenting the inter-disciplinary approach to learning and teaching has resulted in an exploration of the complexities we employ to discover meaning in a range of contexts not singularly reliant on art or language. A convergence is presented in that mathematical rules unite with the rules of art and design in the attempt to project new concepts into new situations where a space for originality exists. Here, the students have been encouraged to imagine new, effective ways of bringing ideas to form (Richmond, 2009). Naturally, developing explicit appreciation/action situations required critical and creative thinking to coincide with lateral and literal approaches to gaining knowledge and understanding of aesthetics. The study presents a reflexive account of the delivery of coursework entitled The Possibilities of the Parabola, from concept to completion.
4
Heyer, Claudius. "Applications of parabolic Hecke algebras: parabolic induction and Hecke polynomials." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/20137.
Повний текст джерелаАнотація:
Im ersten Teil wird eine neue Konstruktion der parabolischen Induktion für pro-p Iwahori-Heckemoduln gegeben. Dabei taucht eine neue Klasse von Algebren auf, die in gewisser Weise als Interpolation zwischen der pro-p Iwahori-Heckealgebra einer p-adischen reduktiven Gruppe $G$ und derjenigen einer Leviuntergruppe $M$ von $G$ gedacht werden kann. Für diese Algebren wird ein Induktionsfunktor definiert und eine Transitivitätseigenschaft bewiesen. Dies liefert einen neuen Beweis für die Transitivität der parabolischen Induktion für Moduln über der pro-p Iwahori-Heckealgebra. Ferner wird eine Funktion auf einer parabolischen Untergruppe untersucht, die als Werte nur p-Potenzen annimmt. Es wird gezeigt, dass sie eine Funktion auf der (pro-p) Iwahori-Weylgruppe von $M$ definiert, und
dass die so definierte Funktion monoton steigend bzgl. der Bruhat-Ordnung ist und einen Vergleich der Längenfunktionen zwischen der Iwahori-Weylgruppe von $M$ und derjenigen der Iwahori-Weylgruppe von $G$ erlaubt.
Im zweiten Teil wird ein allgemeiner Zerlegungssatz für Polynome über der sphärischen (parahorischen) Heckealgebra einer p-adischen reduktiven Gruppe $G$ bewiesen. Diese Zerlegung findet über einer parabolischen Heckealgebra statt, die die Heckealgebra von $G$ enthält. Für den Beweis des Zerlegungssatzes wird vorausgesetzt, dass die gewählte parabolische Untergruppe in einer nichtstumpfen enthalten ist. Des Weiteren werden die nichtstumpfen parabolischen Untergruppen von $G$ klassifiziert.The first part deals with a new construction of parabolic induction for modules over the pro-p Iwahori-Hecke algebra. This construction exhibits a new class of algebras that can be thought of as an interpolation between the pro-p Iwahori-Hecke algebra of a p-adic reductive group $G$ and the corresponding algebra of a Levi subgroup $M$ of $G$. For these algebras we define a new induction functor and prove a transitivity property. This gives a new proof of the transitivity of parabolic induction for modules over the pro-p Iwahori-Hecke algebra. Further, a function on a parabolic subgroup with p-power values is studied. We show that it induces a function on the (pro-p) Iwahori-Weyl group of $M$, that it is monotonically increasing with respect to the Bruhat order, and that it allows to compare the length function on the Iwahori-Weyl group of $M$ with the one on the Iwahori-Weyl group of $G$. In the second part a general decomposition theorem for polynomials over the spherical (parahoric) Hecke algebra of a p-adic reductive group $G$ is proved. The proof requires that the chosen parabolic subgroup is contained in a non-obtuse one. Moreover, we give a classification of non-obtuse parabolic subgroups of $G$.
5
Gantz, Christian. "On parabolic bundles." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320221.
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6
Boger, D. (Dorin). "Parabolic Springer resolution." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104605.
Повний текст джерелаАнотація:
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 73-75).
Let G be a reductive group over a field k = k. Let P be a parabolic subgroup. We construct a functor Groupoid ... is a connected space, which induces an action of generalizing a classical result. It is also a part of a study of natural equivalences between ... for P, Q associated parabolic subgroups.
by D. Boger.
Ph. D.
7
Smorlesi, Anna Sofia <1995>. "Aleksandra Ekster: una parabola del colore." Master's Degree Thesis, Università Ca' Foscari Venezia, 2021. http://hdl.handle.net/10579/20164.
Повний текст джерелаАнотація:
L’intento del presente lavoro è duplice: sottolineare come Aleksandra Ekster abbia rivestito un ruolo di trait d’union tra la nascente avanguardia russa e l’ambiente artistico francese nei primi anni ’10 del XX secolo e come l’innovativo impiego del colore, su una superficie bidimensionale come la tela e in uno spazio tridimensionale come la scena teatrale, sia la chiave di lettura privilegiata attraverso cui prendere in esame l’attività di questa poliedrica artista.
La ricerca si articola in sei capitoli.
I – vengono analizzati i primi esperimenti pittorici della Ekster, che risentono dell’influenza dell’arte popolare ucraina da una parte e degli studi cezanniani sul rapporto tra colore e forma dall’altra.
II – ci si concentra sul primo soggiorno parigino della Ekster, dove l’artista, all’inizio respinta poiché troppo esuberante nel colore, trova una strada autonoma tra le voci del cubismo francese, ma anche del futurismo italiano.
III – si cerca di porre in risalto come la Ekster interagisca con il cubo-futurismo, senza essere ascritta specificamente né all'uno né all'altro movimento.
IV - si analizza come la Ekster riesca, allo scoppio della prima guerra mondiale, a dare comunque il suo originale contributo alle mostre dell'avanguardia russa, e a confrontarsi con il suprematismo di Malevič, ancora in nome del colore.
V – si cerca di dimostrare come la Ekster scommetta sul colore anche nell’attività di scenografa: il colore disegna i corpi degli attori e conferisce loro dinamicità.
VI – nell’ultima parte si vuole porre in evidenza come il colore abbia incontrato la fabbricazione di abiti e la propaganda: alla Ekster viene affidato il compito di veicolare il dinamismo dell’attività di propaganda attraverso le sue capacità cromatiche.
8
Taher, Chadi. "Calculating the parabolic chern character of a locally abelain parabolic bundle : the chern invariants for parabolic bundles at multiple points." Nice, 2011. http://www.theses.fr/2011NICE4013.
Повний текст джерелаАнотація:
In this thesis we calculate the parabolic Chern character of a bundle with locally abelian parabolic structure on a smooth strict normal crossings divisor, using the definition in terms of Deligne-Mumford stacks. We obtain explicit formulas for ch_1, ch_2 and ch_3, and verify that these correspond to the formulas given by Borne for ch_1 and Mochizuki for ch_2. The second part of the thesis we take D subset in X is a curve with multiple points in a surface, a parabolic bundle defined on (X, D) away from the singularities can be extended in several ways to a parabolic bundle on a resolution of singularities. We investigate the possible parabolic Chern classes for these extensions.
9
Schaller, Christian James 1969. "Venus ejecta parabolas: Comparing theory with observation." Thesis, The University of Arizona, 1998. http://hdl.handle.net/10150/278652.
Повний текст джерелаАнотація:
The Magellan radar imager detected approximately 60 dark (i.e. low backscatter cross section) parabola-shaped features on the surface of Venus; each parabola is oriented with the open end toward the west and envelopes an impact crater near its "focus." In this thesis, I use a model of parabola formation to fit the 58 Venusian parabolas observed to date, as well as 9 circular features that are similar to the parabolas. I achieve good results for ∼65% of the 41 parabolas that meet the conditions for the model to apply. As a result of modeling the parabolas, I derive a quantitative description of the distribution of small (∼1 cm to ∼1 μm in diameter) impact ejecta over a planetary surface. My results agree well with the distribution of fine impact ejecta derived for the Terrestrial impact crater Chicxulub. In addition, these results lead to a method for estimating the quantity of fine-grained material available on Venus for surface transport processes such as saltation.
10
Sternesjö, Malin. "Parabolen, biblioteket och spelet." Thesis, Konstfack, Institutionen för Konst (K), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:konstfack:diva-6106.
Повний текст джерелаАнотація:
Jag höll på att inledna med att jag är illojal mot mina medium. Men jag hejdar mig halvvägs, för jag har aldrig gjort några löften. Illojaliteten är inte riktad mot ett medium eller ett tema, utan mot en förväntan på en enhetlig praktik. Vems förväntan? Jag vet inte riktigt vem den tillhör men den har följt mig länge. Vad jag vet är att jag inte har någon lust att konstruera ett konstnärsskap ur en uppsättning handlingar som innehåller lika många olikheter som likheter eller vars likheter med varandra är sinsemellan väldigt olika. När jag tillåter mig att avstå från att formulera en enande tes undervilken mina arbeten ska vila blir det enklare att vara konsekvent och ärlig inom varje arbete. Så jag kommer att tillåta mig att avstå. Jag kommer skriva om saker jag har gjort, saker andra har gjort, tankar jag har tänkt och tankar andra har tänkt.
11
Deolmi, Giulia. "Computational Parabolic Inverse Problems." Doctoral thesis, Università degli studi di Padova, 2012. http://hdl.handle.net/11577/3423351.
Повний текст джерелаАнотація:
This thesis presents a general approach to solve numerically parabolic Inverse Problems, whose underlying mathematical model is discretized using the Finite Element method. The proposed solution is based upon an adaptive parametrization and it is applied specically to a geometric conduction inverse problem of corrosion estimation and to a boundary convection inverse problem of pollution rate estimation.In questa tesi viene presentato un approccio numerico volto alla risoluzione di problemi inversi parabolici, basato sull'utilizzo di una parametrizzazione adattativa. L'algoritmo risolutivo viene descritto per due specici problemi: mentre il primo consiste nella stima della corrosione di una faccia incognita del dominio, il secondo ha come scopo la quanticazione di inquinante immesso in un fiume.
12
Garay, Christopher. "Infinite Hallways: “Parabola Heretica” and Other Journeys." Thesis, University of North Texas, 2013. https://digital.library.unt.edu/ark:/67531/metadc407839/.
Повний текст джерелаАнотація:
This creative thesis collects five fictional stories, as well as a critical preface entitled “Fractals and the Gestalt: the Hybridization of Genre.” The critical preface discusses genre as a literary element and explores techniques for effective genre hybridization. The stories range from psychological fiction to science fiction and fantasy fiction. Each story also employs elements from other genres as well. These stories collectively explore the concept of the other and themes of connection and ostracization.
13
Gombi, Alessandro. "The foundational case of the parabolic motion: design of an interdisciplinary activity for the IDENTITIES project." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21181/.
Повний текст джерелаАнотація:
Questa tesi si inserisce nel campo di ricerca in Didattica della Fisica. In particolare, il lavoro si colloca all’interno del progetto Erasmus+ IDENTITIES, avviato nel settembre 2019, in collaborzione con le università di Montpellier, Creta, Parma e Barcellona. IDENTITIES ha lo scopo di sviluppare moduli didattici interdisciplinari (fisica – matematica – informatica), rivolti ai futuri insegnanti. I moduli riguardano sia temi curricolari sia temi STEM come contesto in cui sviluppare competenze interdisciplinari e progettare nuovi modelli di co-teaching.
I temi di IDENTITIES hanno ispirato e guidato l’attuazione di un corso rivolto a insegnanti di scuola secondaria di secondo grado, organizzato dal PLS di Fisica di Bologna assieme al PLS di Matematica e il POT di Bologna. Il corso, svoltosi tra novembre e dicembre 2019 ha rappresentato la principale fonte di materiale e di riflessioni per questo lavoro.
L’obiettivo di questa tesi è contribuire al progetto tramite la creazione di un’attività didattica, rivolta ai futuri insegnanti, sul tema della parabola e del moto parabolico. L’attività è stata progettata con lo scopo di guidare attraverso i principali passaggi che hanno caratterizzato, da un punto di vista epistemologico, l’evoluzione del pensiero fisico dalla teoria sul moto del proiettile di Tartaglia fino alla dimostrazione della traiettoria parabolica del proiettile di Galileo.
Nella tesi sono descritti il quadro teorico di base per il lavoro, la rielaborazione del materiale del corso PLS per costruire lenti per l’analisi dei libri di testo, l’analisi di un capitolo del libro di testo sulla cinematica bidimensionale e la conseguente progettazione dell’attività didattica. Nelle conclusioni sono discussi i principali risultati ottenuti, tra i quali la produzione delle griglie originali per l’analisi di libri di testo, l’individuazione della simmetria e dell’indipendenza dei moti come attivatori epistemologici e la produzione dell’attività.
14
Bauwe, Anne, and Wilfried Grecksch. "A parabolic stochastic differential inclusion." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501221.
Повний текст джерелаАнотація:
Stochastic differential inclusions can be considered as a generalisation of stochastic
differential equations. In particular a multivalued mapping describes the set
of equations, in which a solution has to be found.
This paper presents an existence result for a special parabolic stochastic inclusion.
The proof is based on the method of upper and lower solutions. In the deterministic
case this method was effectively introduced by S. Carl.
15
Baysal, Arzu. "Inverse Problems For Parabolic Equations." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12605623/index.pdf.
Повний текст джерелаАнотація:
In this thesis, we study inverse problems of restoration of the unknown function in a boundary condition, where on the boundary of the domain there is a convective heat exchange with the environment. Besides the temperature of the domain, we seek either the temperature of the environment in Problem I and II, or the coefficient of external boundary heat emission in Problem III and IV. An additional information is given, which is the overdetermination condition, either on the boundary of the domain (in Problem III and IV) or on a time interval (in
Problem I and II). If solution of inverse problem exists, then the temperature can be defined everywhere on the domain at all instants.
The thesis consists of six chapters. In the first chapter, there is the introduction where the definition and applications of inverse problems are given and definition of the four inverse problems, that we will analyze in this thesis, are stated. In the second chapter, some definitions and theorems which we will use to obtain some conclusions about the corresponding direct problem of our four inverse problems are stated, and the conclusions about direct problem are obtained.
In the third, fourth, fifth and sixth chapters we have the analysis of inverse problems I, II, III and IV, respectively.
16
Eberhardt, Jens Niklas [Verfasser], and Wolfgang [Akademischer Betreuer] Soergel. "Graded and geometric parabolic induction." Freiburg : Universität, 2017. http://d-nb.info/113557216X/34.
Повний текст джерела
17
Alphonse, Amal. "Parabolic PDEs on evolving spaces." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/77658/.
Повний текст джерелаАнотація:
This thesis is concerned with the well-posedness of solutions to certain linear and nonlinear parabolic PDEs on evolving spaces. We first present an abstract framework for the formulation and well-posedness of linear parabolic PDEs on abstract evolving Hilbert spaces. We introduce new function spaces and a notion of a weak time derivative called the weak material derivative for this purpose. We apply this general theory to moving hypersurfaces and Sobolev spaces and study four different linear problems including a coupled bulk-surface system and a dynamical boundary problem. Then we formulate a Stefan problem itself on an evolving surface and consider weak solutions given integrable data through the enthalpy approach, using a generalisation to the Banach space setting of the function spaces introduced in the abstract framework. We finish by studying a nonlocal problem: a porous medium equation with a fractional diffusion posed on an evolving surface and we prove well-posedness for bounded initial data.
18
Sa, Ngiamsunthorn Parinya. "Domain perturbation for parabolic equations." Thesis, The University of Sydney, 2011. http://hdl.handle.net/2123/7775.
Повний текст джерелаАнотація:
We study the effect of domain perturbation on the behaviour of parabolic equations. The first aspect considered in this thesis is the behaviour of solutions under changes of the domain. We show how solutions of linear and semilinear parabolic equations behave as a sequence of domains $\Omega_n$ converges to an open set $\Omega$ in a certain sense. In particular, we are interested in singular domain perturbations so that a change of variables is not possible on these domains. For autonomous linear equations, it is known that convergence of solutions under domain perturbation is closely related to the corresponding elliptic equations via a standard semigroup theory. We show that there is also a relation between domain perturbation for non-autonomous linear parabolic equations and domain perturbation for elliptic equations. The key result for this is the equivalence of Mosco convergences between various closed and convex subsets of Banach spaces. An important consequence is that the same conditions for a sequence of domains imply convergence of solutions under domain perturbation for both parabolic and elliptic equations. By applying variational methods, we obtain the convergence of solutions of initial value problems under Dirichlet or Neumann boundary conditions. A similar technique can be applied to obtain the convergence of weak solutions of parabolic variational inequalities when the underlying convex set is perturbed. Using the linear theory, we then study domain perturbation for initial boundary value problems of semilinear type. We are also interested in the behaviour of bounded entire solutions of parabolic equations defined on the whole real line. We establish a convergence result for bounded entire solutions of linear parabolic equations under $L^2$ and $L^p$-norms. For the $L^p$-theory, we also prove H\"{o}lder regularity of bounded entire solutions with respect to time. In addition, the persistence of some classes of bounded entire solutions is given for semilinear equations using the Leray-Schauder degree theory. The second aspect is to study the dynamics of parabolic equations under domain perturbation. In this part, we consider parabolic equation as a dynamical system in an $L^2$ space and study the stability of invariant manifolds near a stationary solution. In particular, we prove the continuity (upper and lower semicontinuity) of both, the local stable invariant manifolds and the local unstable invariant manifolds under domain perturbation.
19
Floridia, Giuseppe. "Approximate multiplicative controllability for degenerate parabolic problems and regularity properties of elliptic and parabolic systems." Doctoral thesis, Università di Catania, 2012. http://hdl.handle.net/10761/1051.
Повний текст джерелаАнотація:
This thesis consists of two parts, both related to the theory of parabolic equations and systems.
The first part is devoted to control theory which studies the possibility of influencing
the evolution of a given system by an external action called control. Here we address approximate controllability problems via multiplicative controls, motivated by our interest in some differential models for the study of climatology.
In the second part of the thesis we address regularity issues on the local differentiability and H\"older regularity for weak solutions of nonlinear systems in divergence form.
In order to improve readability, the two parts have been organized as completely independent chapters, with
two separate introductions and bibliographies.
All the new results of this thesis have been presented at conferences and workshops, and
most of them appeared or are to appear as research articles in international journals.
Related directions for future research are also outlined in body of the work.
20
Lobkova, Tatiana. "Homogenization Results for Parabolic and Hyperbolic-Parabolic Problems and Further Results on Homogenization in Perforated Domains." Licentiate thesis, Mittuniversitetet, Avdelningen för kvalitetsteknik, maskinteknik och matematik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-30683.
Повний текст джерелаАнотація:
This thesis is based on four papers. The main focus is on homogenization of selected parabolic problems with time oscillations, and hyperbolic-parabolic problems without time oscillations. The approaches are prepared by means of certain methods, such as two-scale convergence, multiscale convergence and evolution multiscale convergence. We also discuss further results on homogenization of evolution problems in perforated domains.Vid tidpunkten för försvar av avhandlingen var följande delarbeten opublicerade: delarbete 1 inskickat, delarbete 2 accepterat, delarbete 4 inskickat.
At the time of the defence the following papers were unpublished: paper 1 submitted, paper 2 accepted, paper 4 submitted.
21
Merchant, Anwar A. "Least square parabola applied to buckling of concrete plates." Thesis, Kansas State University, 1986. http://hdl.handle.net/2097/9937.
Повний текст джерела
22
Dell'Olivo, Caterina <1984>. "LA PARABOLA DELLO STATO NAZIONE DA WESTFALIA AD OGGI." Master's Degree Thesis, Università Ca' Foscari Venezia, 2013. http://hdl.handle.net/10579/3406.
Повний текст джерелаАнотація:
Lo scopo di questo lavoro è di identificare le caratteristiche fondamentali nella storia del moderno stato nazione, capire quale sia il possibile panorama geopolitico globale futuro e la distribuzione del potere tra gli attori internazionali.
Per perseguire questo risultato è importante considare alcuni aspetti pecuilari della storia moderna e contemporanea quali lo sviluppo politico delle strutture di governo sia in Europa che negli Stati Uniti, rispettivamente alla divisione geopolitica risultata dagli accordi di Westfalia.
Inoltre, l'aspetto economico deve essere considerato come deterimante per il mantenimento degli equilibri politici negli ultimi secoli, integrandolo al contesto sociale
23
ASCOLESE, SARA. "SCOMPARIRE DAL MONDO: LA PARABOLA ARTISTICA DI ROBERT WALSER." Doctoral thesis, Università degli Studi di Milano, 2013. http://hdl.handle.net/2434/217808.
Повний текст джерелаАнотація:
Disappearing from the world: Robert Walser's artistic path. The aim of my thesis is to explain why Robert Walser decided to disappear from the real and from the artistic wolrd spending the last thirty years of his life in a psychiatric clinic. Subjects of my thesis are: nonconformity, anti-Bildungsroman, the will to be small and to serve, the walk, the microgramms and the illness and at the end Robert Walser's poetry and style.
24
Yolcu, Türkay. "Parabolic systems and an underlying Lagrangian." Diss., Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29760.
Повний текст джерелаАнотація:
In this thesis, we extend De Giorgi's interpolation method to a class of parabolic equations which are not gradient flows but possess an entropy functional and an underlying Lagrangian. The new fact in the study is that not only the Lagrangian may depend on spatial variables, but also it does not induce a metric. Assuming the initial condition is a density function, not necessarily smooth, but solely of bounded first moments and finite "entropy", we use a variational scheme to discretize the equation in time and construct approximate solutions. Moreover, De Giorgi's interpolation method is revealed to be a powerful tool for proving convergence of our algorithm. Finally, we analyze uniqueness and stability of our solution in L¹.
25
Rael, Michael Brian. "Results on the Parabolic Anderson Model." Thesis, University of California, Irvine, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3562176.
Повний текст джерелаАнотація:
In this dissertation we present various results pertaining to the Parabolic Anderson Model. First we show that the Lyapunov exponent, λ(κ), of the Parabolic Anderson Model in continuous space with Stratonovich differential is O(κ1/3) near 0. We prove the required upper bound, the lower bound having been proven in (Cranston & Mountford 2006).
Second, we prove the existence of stationary measures for the Parabolic Anderson Model in continuous space with Ito differential. Furthermore, we prove that these measures are associated and determined by the average mass of the initial configuration.
Finally we present progress towards computing the Lyapunov exponent of the Quasi-Stationary Parabolic Anderson Model. We prove a smaller upper bound on λ(κ), improving on the work in (Boldrighini, Molchanov, & Pellegrinotti 2007), but our bound is not sharp. Computing λ(κ) in this model remains an open problem.
26
Yung, Tamara. "Traffic Modelling Using Parabolic Differential Equations." Thesis, Linköpings universitet, Kommunikations- och transportsystem, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-102745.
Повний текст джерелаАнотація:
The need of a working infrastructure in a city also requires an understanding of how the traffic flows. It is known that increasing number of drivers prolong the travel time and has an environmental effect in larger cities. It also makes it more difficult for commuters and delivery firms to estimate their travel time. To estimate the traffic flow the traffic department can arrange cameras along popular roads and redirect the traffic, but this is a costly method and difficult to implement. Another approach is to apply theories from physics wave theory and mathematics to model the traffic flow; in this way it is less costly and possible to predict the traffic flow as well. This report studies the application of wave theory and expresses the traffic flow as a modified linear differential equation. First is an analytical solution derived to find a feasible solution. Then a numerical approach is done with Taylor expansions and Crank-Nicolson’s method. All is performed in Matlab and compared against measured values of speed and flow retrieved from Swedish traffic department over a 24 hours traffic day. The analysis is performed on a highway stretch outside Stockholm with no entries, exits or curves. By dividing the interval of the highway into shorter equal distances the modified linear traffic model is expressed in a system of equations. The comparison between actual values and calculated values of the traffic density is done with a nominal average difference. The results reveal that the numbers of intervals don’t improve the average difference. As for the small constant that is applied to make the linear model stable is higher than initially considered.
27
Hofmanová, Martina. "Degenerate parabolic stochastic partial differential equations." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2013. http://tel.archives-ouvertes.fr/tel-00916580.
Повний текст джерелаАнотація:
In this thesis, we address several problems arising in the study of nondegenerate and degenerate parabolic SPDEs, stochastic hyperbolic conservation laws and SDEs with continues coefficients. In the first part, we are interested in degenerate parabolic SPDEs, adapt the notion of kinetic formulation and kinetic solution and establish existence, uniqueness as well as continuous dependence on initial data. As a preliminary result we obtain regularity of solutions in the nondegenerate case under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives. In the second part, we consider hyperbolic conservation laws with stochastic forcing and study their approximations in the sense of Bhatnagar-Gross-Krook. In particular, we describe the conservation laws as a hydrodynamic limit of the stochastic BGK model as the microscopic scale vanishes. In the last part, we provide a new and fairly elementary proof of Skorkhod's classical theorem on existence of weak solutions to SDEs with continuous coefficients satisfying a suitable Lyapunov condition.
28
Dekkers, Sophia Antonia Janna. "Degenerate parabolic equations on Riemannanian manifolds." Thesis, Imperial College London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.405755.
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29
Blanke, Sarah [Verfasser]. "Quasilinear Elliptic-Parabolic Systems / Sarah Blanke." Berlin : epubli, 2017. http://d-nb.info/1124291873/34.
Повний текст джерела
30
Parvin, S. "Diffusion-convection problems in parabolic equations." Thesis, University of Manchester, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382761.
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31
Ribeiro, Saraiva L. M. "Removable singularities and quasilinear parabolic equations." Thesis, University of Sussex, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.356520.
Повний текст джерела
32
Elbirki, Asma. "On parabolic equations with gradient terms." Thesis, University of Sussex, 2016. http://sro.sussex.ac.uk/id/eprint/66012/.
Повний текст джерелаАнотація:
This thesis is concerned with the study of the important effect of the gradient term in parabolic problems. More precisely, we study the global existence or nonexistence of solutions, and their asymptotic behaviour in finite or infinite time. Particularly when the power of the gradient term can increase to the power function of the solution. This thesis consists of five parts. (i) Steady-State Solutions, (ii) The Blow-up Behaviour of the Positive Solutions, (iii) Parabolic Liouville-Type Theorems and the Universal Estimates, (iv) The Global Existence of the Positive Solutions, (v) Viscous Hamilton-Jacobi Equations (VHJ). Under certain conditions on the exponents of both the function of the solution and the gradient term, the nonexistence of positive stationary solution of parabolic problems with gradient terms are proved in (i). In (ii), we extend some known blow-up results of parabolic problems with perturbation terms, which is not too strong, to problems with stronger perturbation terms. In (iii), the nonexistence of nonnegative, nontrivial bounded solutions for all negative and positive times on the whole space are showed for parabolic problems with a strong perturbation term. Moreover, we study the connections between parabolic Liouville-type theorems and local and global properties of nonnegative classical solutions to parabolic problems with gradient terms. Namely, we use a general method for derivation of universal, pointwise a priori estimates of solutions from Liouville type theorems, which unifies the results of a priori bounds, decay estimates and initial and final blow up rates. Global existence and stability, and unbounded global solutions are shown in (iv) when the perturbation term is stronger. In (v) we show that the speed of divergence of gradient blow up (GBU) of solutions of Dirichlet problem for VHJ, especially the upper GBU rate estimate in n space dimensions is the same as in one space dimension.
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Noppakaew, Passawan. "Parabolic projection and generalized Cox configurations." Thesis, University of Bath, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.642047.
Повний текст джерелаАнотація:
Building on the work of Longuet-Higgins in 1972 and Calderbank and Macpherson in 2009, we study the combinatorics of symmetric configurations of hyperplanes and points in projective space, called generalized Cox configurations. To do so, we use the formalism of morphisms between incidence systems. We notice that the combinatorics of Cox configurations are closely related to incidence systems associated to certain Coxeter groups. Furthermore, the incidence geometry of projective space P (V ), where V is a vector space, can be viewed as an incidence system of maximal parabolic subalgebras in a semisimple Lie algebra g, in the special case g = pgl (V ) the projective general linear Lie algebra of V . Using Lie theory, the Coxeter incidence system for the Coxeter group, whose Coxeter diagram is the underlying diagram of the Dynkin diagram of the g, can be embedded into the parabolic incidence system for g. This embedding gives a symmetric geometric configuration which we call a standard parabolic configuration of g. In order to construct a generalized Cox configuration, we project a standard parabolic configuration of type Dn into the parabolic incidence system of projective space using a process called parabolic projection, which maps a parabolic subalgebra of the Lie algebra to a parabolic subalgebra of a lower dimensional Lie algebra. As a consequence of this construction, we obtain Cox configurations and their analogues in higher dimensional projective spaces. We conjecture that the generalized Cox configurations we construct using parabolic projection are nondegenerate and, furthermore, any non-degenerate Cox configuration is obtained in this way. This conjecture yields a formula for the dimension of the space of non-degenerate generalized Cox configurations of a fixed type, which enables us to develop a recursive construction for them. This construction is closely related to Longuet-Higgins’ recursive construction of (generalized) Clifford configurations but our examples are more general and involve the extra parameters.
34
Pang, Huadong. "Parabolic equations without a minimum principle." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/38958.
Повний текст джерелаАнотація:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.Includes bibliographical references (p. 63-64).
In this thesis, we consider several parabolic equations for which the minimum principle fails. We first consider a two-point boundary value problem for a one dimensional diffusion equation. We show the uniqueness and existence of the solution for initial data, which may not be continuous at two boundary points. We also examine the circumstances when these solutions admit a probabilistic interpretation. Some partial results are given for analogous problems in more than one dimension.
by Huadong Pang.
Ph.D.
35
Byrne, Jesse William. "Multifractal Analysis of Parabolic Rational Maps." Thesis, University of North Texas, 1998. https://digital.library.unt.edu/ark:/67531/metadc278398/.
Повний текст джерелаАнотація:
The investigation of the multifractal spectrum of the equilibrium measure for
a parabolic rational map with a Lipschitz continuous potential, φ, which satisfies
sup φ < P(φ)
x∈J(T)
is conducted. More specifically, the multifractal spectrum or spectrum of singularities, f(α) is studied.
36
Yolcu, Türkay. "Parabolic systems and an underlying Lagrangian." Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29760.
Повний текст джерелаАнотація:
Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2010.Committee Chair: Gangbo, Wilfrid; Committee Member: Chow, Shui-Nee; Committee Member: Harrell, Evans; Committee Member: Swiech, Andrzej; Committee Member: Yezzi, Anthony Joseph. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Crooks, Elaine Craig Mackay. "Travelling-wave solutions for parabolic systems." Thesis, University of Bath, 1996. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319218.
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Haglund, El Gaidi Sebastian. "Partially Parabolic Wind Turbine Flow Modelling." Thesis, KTH, Mekanik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-226309.
Повний текст джерелаАнотація:
Climate change is an evermore urging existential treat to the human enterprise. Mean temperature and greenhouse gas emissions have in-creased exponentially since the industrial revolution. But solutions are also mushrooming with exponential pace. Renewable energy technologies, such as wind and solar power, are deployed like never before and their costs have decreased significantly. In order to allow for further transformation of the energy system these technologies must be refined and optimised. In wind energy one important field with high potential of refinement is aerodynamics. The aerodynamics of wind turbines constitutes one challenging research frontier in aerodynamics today. In this study, a novel approach for calculating wind turbine flow is developed. The approach is based on the partially parabolic Navier-Stokes equations, which can be solved computationally with higher efficiency as compared to the fully elliptic version. The modelling of wind turbine thrust is done using actuator-disk theory and the torque is modelled by application of the Joukowsky rotor. A validation of the developed model and force implementation is conducted using four different validation cases. In order to provide value for industrial wind energy projects, the model must be extended to account for turbulence (and terrain in case of onshore projects). Possible candidates for turbulence modelling are parabolic k-ε and explicit Reynolds stress turbulence models. The terrain could possibly be incorporated consistently with the used projection method by altering the finite difference grid layout.
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Bégou, Guillaume. "Prévision de la transition laminaire-turbulent dans le code elsA par la méthode des paraboles." Thesis, Toulouse, ISAE, 2018. http://www.theses.fr/2018ESAE0002/document.
Повний текст джерелаАнотація:
Cette thèse propose la reformulation et l'implantation d'une méthode simplifiée de prévision de la transition laminaire-turbulent naturelle, la méthode des paraboles. Elle s'appuie sur une base de donnée pour fournir une expression analytique des taux d'amplification de perturbations modales de la couche limite. Ces perturbations prennent naissance dans la couche limite à travers un mécanisme de réceptivité, puis connaissent une croissance linéaire suivie d'interactions non-linéaires qui conduisent à la transition vers la turbulence.La méthode du facteur-N permet la prévision de la position de transition en supposant qu'elle a lieu quand l'amplification linéaire totale d'un mode des perturbations a atteint une amplitude critique.L'amplification totale est obtenue en intégrant les taux d'amplifications des perturbations le long de la ligne de courant extérieure à la couche limite.Cette formulation intégrale n'est pas adaptée aux codes RANS et ces travaux proposent une reformulation de la méthode du facteur-N sous forme d'équation de transport, dont le terme source dépend du taux d'amplification des perturbations donné par la méthode des paraboles.Le modèle qui en résulte (N-sigma-P ou NSP) permet de déterminer si un point donné est en amont ou en aval du point de transition et ainsi de prévoir la position de transition, pour des configurations où la transition est déclenchée par des modes longitudinaux (ondes de Tollmien-Schlichting) ou transverses (crossflow)A simplified laminar-turbulent transition prediction method (the so-called parabolas method) is recast into a RANS compatible formulation.The parabolas method is a database approach that gives an estimation of the growth rates of modal perturbations growing in the boundary layer.These perturbations rise through a process called receptivity and undergo a linear modal growth, followed by non-linear interactions that lead to a breakdown to transition. The N-factor (or e-to-N) method predicts the transition location under the assumption that transition occurs when the total linear growth of a mode reaches a prescribed threshold. This total growth is obtained via an integration of a mode's growth rate along the boundary-layer edge streamline. This classical integral formulation is not suitable in a RANS context and is therefore recast into a set of transport equations whose source terms depend on the growth rates given by the parabolas method.The resulting model (N-sigma-P or NSP) predicts if a given point in the flow field is up- or downstream of the transition location. It has been validated for cases where transition was triggered by longitudinal (Tollmien-Schlichting) and crossflow modes
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MANCINO, BENEDETTA. "Camilla Ravera e Margherita Sarfatti: due parabole umane a confronto." Doctoral thesis, Università degli studi del Molise, 2014. http://hdl.handle.net/11695/66245.
Повний текст джерелаАнотація:
La tesi si propone di analizzare i diversi elementi che hanno generato ed agevolato l’emancipazione della condizione femminile in età contemporanea, muovendo dall’età giolittiana ed attraversando quasi l’intero Ventennio, fino ai preparativi del secondo conflitto mondiale. Lo studio inizia da una prospettiva generale per poi focalizzare l’attenzione sul vissuto di Margherita Sarfatti e Camilla Ravera. Attraverso le due parabole individuali, cioè, lo scopo è quello di evidenziare il superamento dell’ormai passata – parafrasando Victoria de Grazia – “eredità liberale”, mediante un’attiva partecipazione alla vita politico-sociale, nonché artistico-culturale della Nazione – anche se non sempre ben accolta dall’uomo “nuovo”.
Con questa ipotesi di lavoro mi sono avvalsa delle fonti reperite presso i seguenti fondi documentali: l’Archivio Centrale dello Stato, l’archivio dell’Istituto Gramsci e l’Archivio del Novecento presso il Museo d’Arte Moderna e Contemporanea, MART, con sede a Rovereto.
Come progettato, grazie alle carte compulsate in questi luoghi mi è stato possibile seguire una sorta di binario parallelo, una specie di confronto permanente tra le parabole umane, culturali e politiche della “piccola grande signora del PCI” – per dirla con le parole di Nora Villa – e dell’ “altra donna del Duce” – come rimarcavano Cannistraro e Sullivan – intrecciando la loro vicenda con quella di osservatori esterni. Questo è stato utile per la ricostruzione di alcune vicende e per effettuare, laddove era fattibile, un confronto al fine di avere una visione il più possibile obiettiva.
La Sarfatti e la Ravera muovono entrambe da convinzioni socialiste. La prima, la “vergine rossa”, le professava fin dagli anni veneziani; la seconda, la riservata piemontese le scopriva invece nella “maturità”. Come è noto, hanno poi preso strade profondamente diverse: Margherita accanto a Benito Mussolini e Camilla nella milizia tra le fila del Partito Comunista d’Italia.
Pertanto, ho cercato di ricostruire alcune dinamiche partendo da un vissuto privato, dandone una percezione anche personale. In altre parole, ciò che ricostruisco è il corso degli eventi in relazione ai personaggi che li hanno vissuti – e alle relative impressioni, sensazioni.
Proprio per questo, ovviamente, la narrazione deve tener conto di un limite intrinseco, poiché la fonte scritta, spesso, non riporta un fatto come è realmente accaduto, ma come l’autore del documento lo percepisce o come lo vuole percepire. In quanto tale, esso è corredato da una distorsione della verità, inevitabile e più o meno intenzionale. Ecco perché nel visionare le carte di cui sono venuta in possesso ho cercato di “guardare”, contemporaneamente, sia dall’esterno che dall’interno, intersecando costantemente i piani e i punti di vista.
Per assolvere a questo compito, in merito all’ex prima donna del Regime, sono stati utilizzati dei documenti dell’ACS – presenti in ridotta quantità perché, appartenendo lei alla fazione “giusta”, non aveva a suo “carico”, come nel caso dei dissidenti, nessun faldone di polizia zeppo di scartoffie bensì delle cartelline dalle modeste dimensioni – ma soprattutto le carte del MART.
Di contro c’era Camilla Ravera. Per ricostruire il suo vissuto ho effettuato un duplice percorso: uno interno, basato cioè su fonti quasi dirette perché appartenute alla protagonista e comunque tramandate dalla sua frazione politica; e l’altro esterno, basato cioè su fonti custodite dagli uffici del Regime e pertanto deformi, in alcune informazioni – nel senso che tutto era guardato secondo l’ottica fascista.
Per quel che ha riguardato, invece, il percorso “interno”, con questa espressione mi riferisco al fatto che la documentazione è appartenuta direttamente alla Ravera o comunque non è soggetta a quel pregiudizio di cui possono risentire le carte custodite presso l’ACS. Si tratta, insomma, di ricerche condotte sempre a Roma, ma presso il “Gramsci”. Presso questa struttura ho compulsato il Fondo Memorie e Testimonianze, relativamente al fascicolo personale di Camilla Ravera, reperendo varie carte riguardanti perlopiù il periodo degli anni ’20 e ’30 che narrano il periodo della segreteria clandestina, dell’arresto nel 1930 e qualche altra vicenda raccontata da lei stessa o da qualche suo “compagno”.
Ad ogni modo, al termine di questo lavoro ciò che si auspica è che si riesca – dall’intreccio delle notizie reperite – ad “impreziosire” questa pagina della storia italiana con qualche elemento di inedito interesse.The Great War is the peak of a radical shift in the world history; in other words, total war and mass society changed, irrevocably, habits and lifestyles, resulting in significant changes in political and social life, economic, financial and cultural aspects. There was no exception about the interaction between the sexes: World War I “redefined” the man- woman relationship, causing many changes in social and familiar dynamics. In this context, the objective of my research is to investigate about those tranformations that allowed the change of women status. The work, in short, is going to analyze the role of woman during fascist period, starting from a general prospect and then focuzed on Camilla Ravera and Margherita Sarfatti’s experiences. Both of them had an intense political and social life: after a common militancy in the Italian Socialist Party, they made different choices: the second forward fascist movement, close to the duce; the first in the ranks of the Italian Communist Party. In other words, with my reconstruction of Sarfatti and Ravera’s biographies, I’m going to focus on an important passage about early italian history: the collapse of the old liberal heritage, the birth of a dictatorship, the struggle against fascism, through the active partecipation of two very interesting women in the political, artistic and cultural events of Italian nation. For this purposes – that are under some aspect unreleased – I’ve examined many sources kept in some italian archives. As regards Sarfatti's Life, my studies are concentrated prevalently on documentations kept at MART (Museo d’Arte Moderna e Contemporanea) in Trento and at A.C.S'. (Archivio Centrale dello Stato) in Rome. As regards Ravera’s biography, besides A.C.S.’ papers, I’ve examined papers that are at Istituto Fondazione “Gramsci” in Roma. From my investigation I’ve discovered some original elements that add important details to the women’s biography. In other words, for the Communist leader an interesting aspects emerged about her arrest and the following political detention. As regards, instead, Margherita Sarfatti, , I’ve discovered an original details reading her diaries. In these pages, she relates – in english, in french and in german language – a lot of facts of her life, expecially some political ones; in short, the pages help us to understand her thought, her ideas, all the “sarfattiana” originality. In conclusion, according with my studies and my analysis, I decided to structuralize my work in three parts: - Women in giolittiana age - The period of the Great War and the “building” of Fascism - Since consolidation of Fascist Regime at preparations of the World War II.
41
Rigoni, Francesca. "Inseguire la Nazione. Ferdinando Martini e la parabola dell'Italia liberale." Doctoral thesis, Università degli studi di Padova, 2010. http://hdl.handle.net/11577/3427361.
Повний текст джерелаАнотація:
The research is about Ferdinando Martini, an Italian politician and intellectual (1841-1928). The question that has justified this research has been the attempt to understand through which ways Martini - a man of the nineteenth century and of Risorgimento as well, son of idea of Nation, of liberals and constitutional ideas - reached fascism faith despite his political and cultural roots, such far from any authoritarian propensity. Was it a sudden conversion? Was it a long durée process? Was the biographical trajectory really contradictory or not? From this question, this research has carried on looking for evidence – far and near – that allow to approach the big break, the big transition in Martini identity. On the basis of this issue, the initial questions have been generalized to the context: was it possible to identify an overall process – underground or superficial – capable of explaining the evolution, or the involution, of the Italian liberal culture and politics?La tesi tratta di Ferdinando Martini, politico e intellettuale italiano vissuto a cavallo tra Ottocento e Novecento (1841-1928). Il lavoro si concentra attorno alle svolte dell'identità culturale e politica del personaggio: depretisiano poi zanardelliano, giolittiano poi anti giolittiano, anti crispino poi crispino, anti colonialista poi colonialista, triplicista anti francese poi anti austriaco e filo francese, letterato che sostiene necessaria l'indipendenza degli ambiti e dei ruoli della politica e dell'intellettualità e al tempo stesso politico la cui attività affonda le radici in un terreno intriso di tendenze intellettuali e culturali, infine liberal democratico di tradizioni risorgimentali poi mussoliniano e fascista. La ricerca analizza ciascuno snodo e ricompone la traiettoria globale dell'identità di Martini inserendola all'interno della più ampia storia nazionale dell'Italia liberale, nel tentativo di cogliere i processi, sotterranei e di superficie, le lunghe durate, le sopravvivenze che collegano i due estremi della storia dell'Italia liberale, il Risorgimento e il fascismo.
42
Fontana, Eleonora. "Maximum Principle for Elliptic and Parabolic Equations." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12061/.
Повний текст джерелаАнотація:
Nel primo capitolo si riporta il principio del massimo per operatori ellittici. Sarà considerato, in un primo momento, l'operatore di Laplace e, successivamente, gli operatori ellittici del secondo ordine, per i quali si dimostrerà anche il principio del massimo di Hopf. Nel secondo capitolo si affronta il principio del massimo per operatori parabolici e lo si utilizza per dimostrare l'unicità delle soluzioni di problemi ai valori al contorno.
43
Brooks, Michael John. "Performance of a parabolic trough solar collector." Thesis, Link to the online version, 2005. http://hdl.handle.net/10019/984.
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44
Zacher, Rico. "Quasilinear parabolic problems with nonlinear boundary conditions." [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=969321899.
Повний текст джерела
45
Liu, Weian, Yin Yang, and Gang Lu. "Viscosity solutions of fully nonlinear parabolic systems." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2621/.
Повний текст джерелаАнотація:
In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3].
46
Takayama, Yuuya. "Nahm’s equations, quiver varieties and parabolic sheaves." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/204570.
Повний текст джерела
47
Keras, Sigitas. "Numerical methods for parabolic partial differential equations." Thesis, University of Cambridge, 1997. https://www.repository.cam.ac.uk/handle/1810/251611.
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48
Tsang, Siu Chung. "Preconditioners for linear parabolic optimal control problems." HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/464.
Повний текст джерелаАнотація:
In this thesis, we consider the computational methods for linear parabolic optimal control problems. We wish to minimize the cost functional while fulfilling the parabolic partial differential equations (PDE) constraint. This type of problems arises in many fields of science and engineering. Since solving such parabolic PDE optimal control problems often lead to a demanding computational cost and time, an effective algorithm is desired. In this research, we focus on the distributed control problems. Three types of cost functional are considered: Target States problems, Tracking problems, and All-time problems. Our major contribution in this research is that we developed a preconditioner for each kind of problems, so our iterative method is accelerated. In chapter 1, we gave a brief introduction to our problems with a literature review. In chapter 2, we demonstrated how to derive the first-order optimality conditions from the parabolic optimal control problems. Afterwards, we showed how to use the shooting method along with the flexible generalized minimal residual to find the solution. In chapter 3, we offered three preconditioners to enhance our shooting method for the problems with symmetric differential operator. Next, in chapter 4, we proposed another three preconditioners to speed up our scheme for the problems with non-symmetric differential operator. Lastly, we have the conclusion and the future development in chapter 5.
49
Schwarzacher, Sebastian. "Regularity for degenerate elliptic and parabolic systems." Diss., Ludwig-Maximilians-Universität München, 2013. http://nbn-resolving.de/urn:nbn:de:bvb:19-162092.
Повний текст джерелаАнотація:
In this work local behavior for solutions to the inhomogeneous p-Laplace in divergence form and its parabolic version are studied. It is parabolic and non-linear generalization of the Calderon-Zygmund theory for the Laplace operator.
I.e. the borderline case BMO is studied. The two main results are local BMO and Hoelder estimates for the inhomogenious p-Laplace and the parabolic p-Laplace system. An adaption of some estimates to fluid mechanics, namely on the p-Stokes equation are also proven. The p-Stokes system is a very important physical model for so-called non Newtonian fluids (e.g. blood). For this system BMO and Hoelder estimates are proven in the stationary 2-dimensional case.
50
Dyer, Luke Oliver. "Parabolic boundary value problems with rough coefficients." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/33276.
Повний текст джерелаАнотація:
This thesis is motivated by some of the recent results of the solvability of elliptic PDE in Lipschitz domains and the relationships between the solvability of different boundary value problems. The parabolic setting has received less attention, in part due to the time irreversibility of the equation and difficulties in defining the appropriate analogous time-varying domain. Here we study the solvability of boundary value problems for second order linear parabolic PDE in time-varying domains, prove two main results and clarify the literature on time-varying domains. The first result shows a relationship between the regularity and Dirichlet boundary value problems for parabolic equations of the form Lu = div(A∇u)−ut = 0 in Lip(1, 1/2) time-varying cylinders, where the coefficient matrix A = [aij(X, t)] is uniformly elliptic and bounded. We show that if the Regularity problem (R)p for the equation Lu = 0 is solvable for some 1 < p < then the Dirichlet problem (D*) 1 p, for the adjoint equation L*v = 0 is also solvable, where p' = p/(p − 1). This result is analogous to the one established in the elliptic case. In the second result we prove the solvability of the parabolic Lp Dirichlet boundary value problem for 1 < p ≤ ∞ for a PDE of the form ut = div(A∇u)+B ·∇u on time-varying domains where the coefficients A = [aij(X, t)] and B = [bi(X, t)] satisfy a small Carleson condition. This result brings the state of affairs in the parabolic setting up to the current elliptic standard. Furthermore, we establish that if the coefficients of the operator A and B satisfy a vanishing Carleson condition, and the time-varying domain is of VMO-type then the parabolic Lp Dirichlet boundary value problem is solvable for all 1 < p ≤ ∞. This is related to elliptic results where the normal of the boundary of the domain is in VMO or near VMO implies the invertibility of certain boundary operators in Lp for all 1 < p < ∞. This then (using the method of layer potentials) implies solvability of the Lp boundary value problem in the same range for certain elliptic PDE. We do not use the method of layer potentials, since the coefficients we consider are too rough to use this technique but remarkably we recover Lp solvability in the full range of p's as the elliptic case. Moreover, to achieve this result we give new equivalent and localisable definitions of the appropriate time-varying domains.