Dissertations / Theses on the topic 'Ntegral equation for the non'
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Daviau, Claude. "Equation de dirac non lineaire." Nantes, 1993. http://www.theses.fr/1993NANT2006.
Full textHatimy, Abdelhalim. "Comportement des solutions d'un oscillateur non autonome a non linearites quadratiques." Toulouse, INSA, 1986. http://www.theses.fr/1986ISAT0016.
Full textSili, Ali. "Deux problèmes d'évolution non linéaires." Paris 6, 1987. http://www.theses.fr/1987PA066113.
Full textKedge, Christopher J. "A new non-cubic equation of state." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0017/MQ49698.pdf.
Full textOswald, Luc. "Etude de problemes non lineaires avec singularites." Paris 6, 1987. http://www.theses.fr/1987PA066060.
Full textФедчишина, Ірина Юріївна. "Уточнення апроксимації де Вілдера для оцінки ймовірності банкрутства у страховій моделі Крамера-Лундберга." Master's thesis, Київ, 2018. https://ela.kpi.ua/handle/123456789/23449.
Full textIn the master's thesis a new approach to the approximate finding of the ruin probability of an insurance company on an infinite time horizon is proposed. The need for such an approximate finding is due to the fact that the exact value of the ruin probability, being a solution to a complex integral equation, can often not be expressed in explicit analytical form. The idea of the developed method is to replace the process of risk with another risk process with insurance payments distributed according to the law, which is a mixture of two exponential distributions. For such a risk process, the ruin probability is known in analytical form. Replacement is realized by equating the first five cumulants of the initial and new risk processes.
В магистерской диссертации предложен новый поход к приближенному нахождению вероятности банкротства страховой компании на бесконечном временном горизонте. Необходимость такого приближенного нахождения обусловлено тем, что точное значение вероятности банкротства, будучи решением сложного интегрального уравнения, часто не может быть выражено в явной аналитической форме. Идея разработанного метода заключается в замене процесса страхового риска на другой процесс риска со страховыми выплатами, распределенными по закону, который является смесью двух экспоненциальных распределений. Для такого процесса риска вероятность банкротства известна в аналитической форме. Замена реализуется путем приравнивания первых пяти кумулянтов начального и нового процессов риска.
Rey, Olivier. "Équations elliptiques non linéaires avec l'exposant critique de Sobolev." Palaiseau, Ecole polytechnique, 1989. http://www.theses.fr/1989EPXX0009.
Full textBacha, Inès. "Traitement symbolique des systèmes d'équations différentielles non linéaires au voisinage des singularités." Université Joseph Fourier (Grenoble), 1997. http://www.theses.fr/1997GRE10078.
Full textMouzaoui, Lounès. "Régimes asymptotiques pour l'équation de Schrödinger non linéaire non locale." Thesis, Montpellier 2, 2013. http://www.theses.fr/2013MON20241/document.
Full textThis thesis is devoted to the study of some asymptotic regimes of the semi-classical Schrödinger equation, in the presence of a nonlocal nonlinearity of Hartree-type . The purpose of the first part, consisting of the first and second chapter is the study of the asymptotic behavior of the previous model with a singular kernel around the origin for an initial data asymptotically of WKB-type, in a weakly nonlinear regime. In the first chapter we show that under some regularity conditions on the initial data, the solution still is of WKB-type at leading order, a result that we get in the functional framework of the Wiener algebra . We give an alternative proof to the previous result in the particular case of the Schrödinger-Poisson equation in the functional framework of rescaled Sobolev space, where the consideration of correctors is necessary to construct an approximate solution to describe the solution at leading order.The second part of this thesis, the subject of the third chapter is devoted to the study the propagation of wave packets for a coupled system of Hartree equations in a semi-classical regime , in the presence of sub-quadratic external potentials. We describe analytically and numerically the asymptotic behavior of the leading order of the wave functions solution of the system, for an initial data in the form of wave packets for different sizes of nonlinearity.The final part consists of the fourth chapter and appendix.In the fourth chapter we consider the Cauchy problem of the Hartree equation with a homogeneous kernel or of Fourier transform in a Lebesgue space, in the functional framework of the Wiener algebra. We show some results on the well-posedness of the problem for the considered kernels, in spaces involving the Wiener algebra.We conclude with an appendix in which we consider the Cauchy problem for the Schrödinger-Poisson equation in the presence of a time independent external potential in the weighted Sobolev spaces. We extend the results already obtained on the existence of global solutions in Sobolev spaces without weight when the external potential is reduced to zero, by showing the existence of global solutions in time in the weighted Sobolev spaces for all regularity
Mehraban, Arash. "Non-Classical Symmetry Solutions to the Fitzhugh Nagumo Equation." Digital Commons @ East Tennessee State University, 2010. https://dc.etsu.edu/etd/1736.
Full textMazzieri, Ilario. "Non-conforming high order methods for the elastodynamics equation." Nice, 2012. http://www.theses.fr/2012NICE4014.
Full textIn this thesis, we present a new discretization approach to combine the Discontinuous Galerkin Spectral Element (DGSE) and the Mortar Spectral Element (MSE) methods with suitable time advancing schemes for the simulation of the elastic wave propagation in heterogeneous media. To overcome the limitations of the existing approaches we apply the non-conforming paradigm only at the subdomain level. We show that the resulting formulations are stable, enjoy optimal approximation properties, and suffer from low dispersion and dissipation errors. Applications of the DGSE and MSE methods to simulate realistic seismic wave propagation problems in three dimensions are also considered
Rakesh, Arora. "Fine properties of solutions for quasi-linear elliptic and parabolic equations with non-local and non-standard growth." Thesis, Pau, 2020. http://www.theses.fr/2020PAUU3021.
Full textIn this thesis, we study the fine properties of solutions to quasilinear elliptic and parabolic equations involving non-local and non-standard growth. We focus on three different types of partial differential equations (PDEs).Firstly, we study the qualitative properties of weak and strong solutions of the evolution equations with non-standard growth. The importance of investigating these kinds of evolutions equations lies in modeling various anisotropic features that occur in electrorheological fluids models, image restoration, filtration process in complex media, stratigraphy problems, and heterogeneous biological interactions. We derive sufficient conditions on the initial data for the existence and uniqueness of a strong solution of the evolution equation with Dirichlet type boundary conditions. We establish the global higher integrability and second-order regularity of the strong solution via proving new interpolation inequalities. We also study the existence, uniqueness, regularity, and stabilization of the weak solution of Doubly nonlinear equation driven by a class of Leray-Lions type operators and non-monotone sub-homogeneous forcing terms. Secondly, we study the Kirchhoff equation and system involving different kinds of non-linear operators with exponential nonlinearity of the Choquard type and singular weights. These type of problems appears in many real-world phenomena starting from the study in the length of the string during the vibration of the stretched string, in the study of the propagation of electromagnetic waves in plasma, Bose-Einstein condensation and many more. Motivating from the abundant physical applications, we prove the existence and multiplicity results for the Kirchhoff equation and system with subcritical and critical exponential non-linearity, that arise out of several inequalities proved by Adams, Moser, and Trudinger. To deal with the system of Kirchhoff equations, we prove new Adams, Moser and Trudinger type inequalities in the Cartesian product of Sobolev spaces.Thirdly, we study the singular problems involving nonlocal operators. We show the existence and multiplicity for the classical solutions of Half Laplacian singular problem involving exponential nonlinearity via bifurcation theory. To characterize the behavior of large solutions, we further study isolated singularities for the singular semi linear elliptic equation. We show the symmetry and monotonicity properties of classical solution of fractional Laplacian problem using moving plane method and narrow maximum principle. We also study the nonlinear fractional Laplacian problem involving singular nonlinearity and singular weights. We prove the existence, uniqueness, non-existence, optimal Sobolev and Holder regularity results via exploiting the C^1,1 regularity of the boundary, barrier arguments and approximation method
JANANE, JILALI. "Existence des solutions de certaines equations non-lineaires du type schroedinger." Rennes 1, 1989. http://www.theses.fr/1989REN10041.
Full textSkelton, P. L. I. "Non-central potentials and inverse methods of the Schroedinger equation." Thesis, University of Hull, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.383686.
Full textDu, Rand Marlie. "Practical equation of state for non-spherical and asymmetric systems." Thesis, Stellenbosch : University of Stellenbosch, 2004. http://hdl.handle.net/10019.1/16043.
Full textENGLISH ABSTRACT: In this study an equation of state has been developed for the specific purpose of representing systems of simple non-polar spherical and chain-like components and their mixtures for practical applications. To be applied in engineering calculations, the model has to be accurate, be able to represent mixtures with large size asymmetry without the use large binary interaction parameters, and be mathematically simple enough to ensure rapid computations. The model is developed through a sequential evaluation of the statistical mechanical theory of particles and the various approaches available to extend it to real fluid systems. The equation of state developed in this work models the real fluid systems as interacting with a highly simplified two step potential model. The repulsive interactions are represented by a newly developed simplified form of the hard sphere equation of state, capable of representing the known hard sphere virial coefficients and phase behaviour to a high degree of accuracy. This equation has a realistic closest packed limiting density in between the idealised hard sphere fluid random and crystal structure limits. The attractive interactions between the particles are incorporated into the model through a perturbation expansion represented in the form of a double summation perturbation approximation. The perturbation matrix was optimised to have the lowest order in density necessary to still be able to accurately represent real fluid properties. In a novel approach to obtain simple mixing rules that result in the theoretically correct second virial coefficient composition dependence, the perturbation matrix is constrained in such a manner that only the first perturbation term has a term that is first order in density. From a detailed evaluation of the various methods available to represent chain-like non-spherical systems it was finally concluded that the Perturbed Hard Chain Theory provided an ideal compromise between model simplicity and accuracy, and this method is used to extend the equation to chain-like systems. Finally the model is extended to fluid mixtures by uniquely developed mixing rules resulting in the correct mixture composition dependence both at low and high system densities. The newly developed equation of state is shown to be capable of representing the pure component systems to a comparable degree of accuracy as the generally applied equations of state for non-spherical systems found in the literature. The proposed equation is furthermore also shown equal or improve on the predictive ability of these models in the representation offluid mixtures consisting out of similar chainlike or size and energetic asymmetric components. Finally, the computational time required to model the behaviour of large multi-component fluid mixtures using the new equation of state is significantly shorter that that of the other semi-empirical equations of state currently available in the literature.
AFRIKAANSE OPSOMMING: Hierdie werkstuk behels die ontwikkeling van ‘n toestandsvergelyking wat spesifiek gerig is op toepassings in alledaagse, praktiese ingenieurstipe berekeninge en daartoe instaat is om sisteme bestaande uit nie-polêre spferiese- en ketting-tipe komponente en hulle mengsels teKettingteorie (PHCT) die mees geskikde metode is vir hierdie doel en is op die vergelyking toegepas. As ‘n laaste stap in die toestandsvergelykingontwikkelling is daar mengreëls ontwikkel vir die vergelyking wat die korrekte samestellingsafhanklikheid toon vir beide die lae en hoë digtheidskondisies. Die model wat in hierdie studie ontwikkel is, is met verskeie ander bekende toestandsvergelykings, wat daartoe instaat is om nie-spferiese sisteme te modelleer, vergelyk en daar is gevind dat die nuwe model daartoe instaat is om suiwer sisteme net so goed as die bestaande vergelykings te modelleer. Verder is daar ook gevind dat die nuwe vergelyking die modellering van verskeie mensels van kettingtipe komponente en komponente van uiteenlopende groottes of interaksie energieë kan ewenaar of verbeter. Laastens is daar ook gevind dat die tyd nodig vir die modellering van die termodinamiese gedrag van mengsels van ‘n groot hoeveelheid komponente aansienlik korter is vir die nuwe model as die ander bekende semi-empiriese vergelykings. kan beskyf. Om aan hierdie vereistes te voldoen moet die toestandsvergelyking die relevante sisteme akkuraat kan modelleer, slegs klein interaksie parameters benodig om mengsels van komponente met groot verskille in molekulêre groottes akkuraat voor te stel en steeds wiskundig eenvoudig genoeg wees om vinnige berekeninge te verseker. Die vergelyking is ontwikkel deur ‘n sistematiese evaluering van die statisitiese meganiese teorie van partikels en die verskillende metodes om hierdie teorië op werklike sisteme toe te pas. Die toestandsvergelyking beskryf die intermolekulêre interaksie tussen die verskillende komponente met ‘n hoogs vereenvoudigde twee-stap interaksie potensiaal model. Die afstotende kragte tussen die komponente word in ag geneem deur ‘n nuwe vergelyking wat ontwikkel is om die gedrag van ‘n ideale harde spfeer sisteem te modelleer. Hierdie hardespfeermodel is daartoe instaat om die viriale koeffisiënte en die fase gedrag van teoretiese harde spfeer sisteme akkuraat te modelleer, en het ‘n maksimum digtheidslimiet wat tussen teoretiese waardes van ‘n perfek geordende en nie-geordende harde spheer sisteem lê. Die aantrekkinskragte tussen die partikels word beskou as ‘n perturbasie van die harde-spheer vergelyking. ‘n Term bestaande uit ‘n dubbelle sommasiefunksie word gebruik om hierdie perturbasie uitbreiding voor te stel. Die sommasie term is geoptimiseer sodat die finale toestandsvergelyking die laagste digtheidsgraad het wat steeds tot ‘n akkurate voorstelling van die termodinamiese gedrag van werklike sisteme lei. Die sommasiefunksie is so gespesifiseer dat die eerste term van die perturbasie uitbreiding slegs ‘n eerste graadse orde in digtheid het in ‘n unieke benadering om te verseker dat die mengreëls van die toestandsvergelyking die teoreties korrekte samestellingafhanklikheid van die mengselvirialekoeffisiente tot gevolg het. ‘n Deeglike ondersoek van die verskillende metodes om die toepassing van die toestandsvergelyking uit te brei tot die moddellering van nie-spheriese ketting-tipe molekules is gedoen en daar is uiteindelik tot die gevolgtrekking gekom dat die Geperturbeerde Harde
THOMPSON, RONEY LEON. "PERFORMANCE OF A NEW CONSTITUTIVE EQUATION FOR NON NEWTONIAN LIQUIDS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2001. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=18975@1.
Full textNon-Newtonian materials exhibit different behavior if submitted to shear or extension. A constitutive equation in wich the stress is a function not only of the rate of deformation, but also of the type of the flow is proposed and analyzed theorecticaly. It combines information obtained in shear, extension and rigid body motion in all regions of a complex flow. This equation is tested with numerical codes for two different axissymmetrical geometries, namely, the 4:1 abrupt contraction and the R(2)z=C convergent channel. Both geometries have been employed to measure the extensional viscosity. In order to validate the model, a test section was buit with a 4:1 contraction. Newtonian and viscoelastic fluids were tested using the Particle Image Velocimetry technique to determine the velocity field.
Loines, J. "Boundary integral equation methods for problems in non-linear magnetostatics." Thesis, Imperial College London, 1985. http://hdl.handle.net/10044/1/37768.
Full textChoulli, Mourad. "Identifiabilite d'un parametre dans une equation parabolique non lineaire monodimensionnelle." Toulouse 3, 1987. http://www.theses.fr/1987TOU30245.
Full textCaudrelier, Vincent. "Equation de Schrödinger non-linéaire et impuretés dans les systèmes intégrables." Phd thesis, Chambéry, 2005. http://tel.archives-ouvertes.fr/tel-00009612.
Full textDans ce contexte, l'équation de Schrödinger non-linéaire (à 1+1 dimensions) est un système privilégié. On la retrouve comme modèle de phénomènes variés tant classiques (optique non-linéaire, mécanique des fluides...) que quantiques (gaz ultra-froids, condensation de Bose-Einstein...). En outre, elle a contribué à la mise au point de techniques de résolution des systèmes intégrables : méthode de diffusion inverse, ansatz de Bethe, identification et utilisation de symétries (groupes quantiques, Yangiens). En utilisant ce système à la fois comme support de test et comme modèle de prédiction, mon travail de thèse tourne autour de deux points principaux :
- Inclusion de degrés de liberté bosoniques et fermioniques.
- Inclusion d'un bord ou d'une impureté.
Dans un premier temps, j'ai étudié une version « supersymétrique » de cette équation pour laquelle j'ai montré la validité de tous les résultats d'intégrabilité, de symétrie et de résolution explicite classiques et quantiques connus pour la version scalaire originelle. La question de l'inclusion d'un bord a été traitée d'un autre point de vue. L'idée est de partir d'une algèbre de symétrie caractéristique des systèmes intégrables avec bord, l'algèbre de réflexion, et de construire un Hamiltonien général intégrable et possédant cette algèbre comme structure de symétrie. Un cas particulier de l'Hamiltonien intégrable obtenu n'est autre que l'Hamiltonien de Schrödinger non-linéaire en présence d'un bord. Un autre cas particulier est l'Hamiltonien de Sutherland en présence d'un bord pour lequel la symétrie n'était pas connue.
Le problème de l'inclusion d'une impureté dans un système intégrable a constitué la plus grosse partie de mon travail. J'ai pu montrer qu'il est possible de préserver l'intégrabilité d'un système avec interaction lorsqu'on introduit un défaut qui transmet et réfléchit (une impureté) grâce à une nouvelle structure algébrique, l'algèbre de Réflexion-Transmission, appliquée à l'équation de Schrödinger non-linéaire. Cela permet de trouver la forme explicite du champ, de calculer de façon exacte les éléments de la matrice de diffusion et les fonctions de corrélation à N points et d'identifier la symétrie du problème.
Suite à ce travail, les équations exactes qui régissent le spectre d'énergie d'un gaz de particules en interaction de contact et en présence d'une impureté contrôlée par quatre paramètres ont été établies. Ces résultats ouvrent des perspectives d'applications en physique de la matière condensée.
Schulze, Bert-Wolfgang, and Yuming Qin. "Uniform compact attractors for a nonlinear non-autonomous equation of viscoelasticity." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/2989/.
Full textLewandowski, Roger. "A propos d'une equation elliptique non lineaire avec un exposant critique." Paris 6, 1990. http://www.theses.fr/1990PA066212.
Full textFlorchinger, Patrick Michel Dominique. "FILTRAGE NON LINEAIRE AVEC BRUITS CORRELES ET OBSERVATION NON BORNEE ETUDE NUMERIQUE D'UNE EQUATION DE ZAKAI /." [S.l.] : [s.n.], 1989. ftp://ftp.scd.univ-metz.fr/pub/Theses/1988/Florchinger.Patrick.SMZ891.pdf.
Full textControzzi, Davide. "Non perturbative aspects of strongly correlated electron systems." Thesis, University of Oxford, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.343661.
Full textRedwane, Hicham. "Solutions normalisées de problèmes paraboliques et elliptiques non linéaires." Rouen, 1997. http://www.theses.fr/1997ROUES059.
Full textLi, Shenghao. "Non-homogeneous Boundary Value Problems for Boussinesq-type Equations." University of Cincinnati / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1468512590.
Full textTarhini, Rana. "Équation de films minces fractionnaire pour les fractures hydrauliques." Thesis, Paris Est, 2018. http://www.theses.fr/2018PESC1061/document.
Full textIn this thesis, we study two degenerate, non-local parabolic equations, a fractional thin film equation and a fractional porous medium equation. The introduction contains a presentation of problems, the previous results in the literature and a brief presentation of our results. In the second chapter, we present a short overview of the De Giorgi method used to prove Hölder regularity of solutions of elliptic equations. Moreover, we present the results using this approach in the local and non-local parabolic cases. In the third chapter we prove existence of weak solutions of a fractional thin film equation. It is a non-local degenerate parabolic equation of order $alpha + 2$ where $0 < alpha < 2$. It is a generalization of an equation studied by Imbert and Mellet in 2011 for $alpha = 1$. To construct these solutions, we consider a regularized problem then we pass to the limit using Sobolev embedding theorem, that's why we distinguish two cases $0 < alpha < 1$ and $1 leq alpha < 2$. We also prove that the solution is positive if the initial condition is so. The fourth chapter is dedicated for a fractional porous medium equation. We prove Hölder regularity of positive weak solutions satisfying energy estimates. First, we prove the existence of weak solutions that satisfy energy estimates. We distiguish two cases $0 < alpha < 1$ and $1 leq alpha < 2$ because of divergence problems. The we prove De Giorgi Lemmas about oscillation reduction from above and from below. This is not suffisant. We need to improve the lemma about oscillation reduction from above. So we pass by an intermediate values lemma and we prove an improved oscillation reduction lemma from above. Finally, we prove Hölder regularity of solutions using the scaling property
Scheidt, Torsten. "Non-linear optical diagnostics of non-centrosymmetric opto-electronic semiconductor materials." Thesis, Stellenbosch : University of Stellenbosch, 2006. http://hdl.handle.net/10019.1/17332.
Full textBonnefille, Max. "Propagation des oscillations dans les systèmes hyperboliques de lois de conservation." Saint-Etienne, 1987. http://www.theses.fr/1987STET4008.
Full textNi, Ying. "Perturbed Renewal Equations with Non-Polynomial Perturbations." Licentiate thesis, Mälardalen University, School of Education, Culture and Communication, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-9354.
Full textThis thesis deals with a model of nonlinearly perturbed continuous-time renewal equation with nonpolynomial perturbations. The characteristics, namely the defect and moments, of the distribution function generating the renewal equation are assumed to have expansions with respect to a non-polynomial asymptotic scale: $\{\varphi_{\nn} (\varepsilon) =\varepsilon^{\nn \cdot \w}, \nn \in \mathbf{N}_0^k\}$ as $\varepsilon \to 0$, where $\mathbf{N}_0$ is the set of non-negative integers, $\mathbf{N}_0^k \equiv \mathbf{N}_0 \times \cdots \times \mathbf{N}_0, 1\leq k <\infty$ with the product being taken $k$ times and $\w$ is a $k$ dimensional parameter vector that satisfies certain properties. For the one-dimensional case, i.e., $k=1$, this model reduces to the model of nonlinearly perturbed renewal equation with polynomial perturbations which is well studied in the literature. The goal of the present study is to obtain the exponential asymptotics for the solution to the perturbed renewal equation in the form of exponential asymptotic expansions and present possible applications.
The thesis is based on three papers which study successively the model stated above. Paper A investigates the two-dimensional case, i.e. where $k=2$. The corresponding asymptotic exponential expansion for the solution to the perturbed renewal equation is given. The asymptotic results are applied to an example of the perturbed risk process, which leads to diffusion approximation type asymptotics for the ruin probability. Numerical experimental studies on this example of perturbed risk process are conducted in paper B, where Monte Carlo simulation are used to study the accuracy and properties of the asymptotic formulas. Paper C presents the asymptotic results for the more general case where the dimension $k$ satisfies $1\leq k <\infty$, which are applied to the asymptotic analysis of the ruin probability in an example of perturbed risk processes with this general type of non-polynomial perturbations. All the proofs of the theorems stated in paper C are collected in its supplement: paper D.
Godinho, Pereira David. "Contribution à l'étude des équations de Boltzmann, Kac et Keller-Segel à l'aide d'équations différentielles stochastiques non linéaires." Phd thesis, Université Paris-Est, 2013. http://tel.archives-ouvertes.fr/tel-00975091.
Full textMawah, Bernard. "Option pricing with transaction costs and a non-linear Black-Scholes equation." Thesis, Uppsala University, Department of Mathematics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-120920.
Full textCostas, Basin Miguel Antonio. "Equation of state and structure in non-electrolyte liquids and their mixtures." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=71982.
Full textWijewardena, Udagamge. "Iterative method of solving schrodinger equation for non-Hermitian, pt-symmetric Hamiltonians." DigitalCommons@Robert W. Woodruff Library, Atlanta University Center, 2016. http://digitalcommons.auctr.edu/dissertations/3194.
Full textPalasciano, Mario. "On a non-local transport equation with competing attraction and Newtonian repulsion." Thesis, McGill University, 2013. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=119401.
Full textNous étudions l'équation d'agrégation $ \rho_t + \nabla \cdot (\rho (- \nabla K \ast \rho)) = 0 $ dans $ \Real^n $, une équation de transport non linéaire et non locale du premier ordre utilisée pour modéliser le comportement d'essaims. Le potentiel d'interaction radial $K$ est choisi pour modéliser à la fois la répulsion à courte portée et l'attraction à longue portée. Nous montrons que les équations sont globalement bien posées en utilisant la méthode des trajectoires de particules, une technique utilisée entre autre pour démontrer l'existence et l'unicité de l'équation d'Euler. Plus précisément, le noyau d'interaction est choisi afin de calculer une solution analytique de la densité le long de trajectoires de particules et pour faire usage de la théorie bien développée des opérateurs intégraux singuliers.Nous démontrons également que les solutions ayant une densité initiale radialement symétrique à support compact $\rho_0 $ demeurent radialement symétriques pour tout temps et approchent asymptotiquement un état stable constitué d'une boule dans $ \Real^n $ avec densité uniforme.
Nathanson, Ekaterina Sergeyevna. "Path integration with non-positive distributions and applications to the Schrödinger equation." Diss., University of Iowa, 2014. https://ir.uiowa.edu/etd/1370.
Full textLindquist, Joseph M. "Unstructured high-order galerkin-temporal-boundary methods for the klein-gordon equation with non-reflecting boundary conditions." Monterey, California : Naval Postgraduate School, 2010. http://edocs.nps.edu/npspubs/scholarly/dissert/2010/Jun/10Jun%5FLindquist%5FPhD.pdf.
Full textDissertation supervisor(s): Neta, Beny ; Giraldo, Francis. "June 2010." Description based on title screen as viewed on July 15, 2010. Author(s) subject terms: Non-reflecting Boundary, Spectral Elements, Runge-Kutta, High-Order, Klein-Gordon, Shallow Water Equations. Includes bibliographical references (p. 145-150). Also available in print.
Nguyen, Vinh Q. "A Numerical Study of Burgers' Equation With Robin Boundary Conditions." Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/31285.
Full textMaster of Science
Hoernel, Jean-David. "Etudes théorique et numérique d'un modèle non-stationnaire de catalyseurs à passages cylindriques." Phd thesis, Université de Haute Alsace - Mulhouse, 2002. http://tel.archives-ouvertes.fr/tel-00002403.
Full textNous établissons l'existence et l'unicité de la solution, ainsi que quelques propriétés qualitatives de cette solution, en particulier l'existence de bornes supérieures et inférieures. Nous étudions également le comportement limite de la solution quand le temps tend vers l'infini.
Nous mettons ensuite en oeuvre une méthode numérique permettant d'obtenir des courbes décrivant le comportement de la solution.
Schumacher, Timothy. "Removable boundary singularities for the equation delta u = uâlpha in non-smooth domains." Connect to online resource, 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3315836.
Full textSikorav, Jacques. "Sur l'identification et la modélisation de phénomènes non-stationnaires en acoustique : Equation des ondes dans les ouverts non-cylindriques." Paris 9, 1988. http://www.theses.fr/1988PA090029.
Full textLee, Huaiqian. "Flots quasi-invariants associés aux champs de vecteur non réguliers." Thesis, Dijon, 2011. http://www.theses.fr/2011DIJOS100/document.
Full textThe thesis mainly consists of two parts.In the first part, we study the quasi-invariant flow generated by the Stratonovich stochas-tic differential equation with BV drift coefficients in the Euclidean space. We generalizethe results of Ambrosio [Invent. Math. 158 (2004), 227{260] on the existence, uniquenessand stability of regular Lagrangian flows of ordinary differential equations to Stratonovichstochastic differential equations with BV drift coefficients. As an application of the sta-bility result, we construct an explicit solution to the corresponding stochastic transportequation in terms of the stochastic flow. The approximate differentiability of the flow isalso studied when the drift coefficient has some Sobolev regularity.In the second part, we generalize the DiPerna-Lions theory in the Euclidean space to thecomplete Riemannian manifold. We define the commutator on the complete Riemannianmanifold which is a probabilistic version of the one in the DiPerna-Lions theory, andestablish the commutator estimate by the probabilistic method. As a direct applicationof the commutator estimate, we investigate the uniqueness of solutions to the transportequation by the method of the renormalized solution. Following Ambrosio's method, weconstruct the DiPerna-Lions flow on the Riemannian manifold. In order to construct thediffusion process associated to an elliptic operator with irregular drift on the completeRiemannian manifold, we give some conditions which guarantee the strong completenessof the horizontal flow. Finally, we construct the diffusion process with the drift coefficienthaving only Sobolev regularity.Besides, we present a brief introduction of the classical theory on the ordinary differentialequation in the smooth case and the quasi-invariant flow of homeomorphisms under theOsgood condition before the first part; and we recall some basic tools and results whichare widely used throughout the whole thesis after the second part
Wilhelm, Spencer Christian. "Prediction of Non-Resting Energy Expenditure using Accelerometry." Thesis, Virginia Tech, 2019. http://hdl.handle.net/10919/91463.
Full textMaster of Science
Accurate measurement of the total amount of energy (i.e. calories) utilized by the body throughout the day, also known as total energy expenditure, is a vital component of metabolic research. However, there is a lack of measurement methods that are valid, objective, inexpensive, and easy to use. Accelerometers combined with equations designed to predict total energy expenditure may be able to fill this gap. Accelerometers are devices worn on the body that measure accelerative forces from physical activity. Twenty weight stable adults (12 female, 8 male), who recently participated in a study in which all dietary intake and exercise were closely monitored (controlled feeding study), comprised the study sample. The amount of energy needed to maintain weight (total energy requirements) was assessed from the controlled feeding period in which weight stability was achieved. Resting energy expenditure, the energy burned while the body is at rest, was assessed using an equation often used to estimate energy expenditure, the Mifflin-St. Jeor equation. Participants wore accelerometers to objectively assess habitual physical activity. The accelerometer data obtained along with subjects’ demographic (age, sex) and biometric (height, weight, BMI, etc.) data were used to predict non-resting energy expenditure (resting energy expenditure subtracted from total energy expenditure). Multiple statistical tests were used to determine the validity of the total energy requirements obtained from the sum of the predicted non-resting energy expenditure (NREE) and resting energy expenditure. Estimated resting energy expenditure was compared with the total energy requirements assessed using the intake-balance method from the controlled feeding period. The resulting prediction equation is as follows: 480.93 – 180.69(sex) + 0.21(Accelerometer kcals) + 617.98(BF%) = NREE. The sex was coded as 1 for females and 0 for males. This prediction model has a coefficient of determination of 0.74 (0.70 adjusted), which means 70% of the variation in non-resting energy expenditure was explained by changes in the variables in the equation. On average, the model overestimates NREE by 76 Calories per day. This new model could be the key to accurately, inexpensively and objectively measuring total energy requirements.
Kyal, Malika El. "Les methodes paralleles asynchrones de multi-decomposition appliquees aux systemes differentiels algebriques non lineaires d'indice inferieur ou egal a 1." Besançon, 1999. http://www.theses.fr/1999BESA2049.
Full textMirrahimi, Mazyar. "Estimation et contrôle non-linéaire : application à quelques systèmes quantiques et classiques." Habilitation à diriger des recherches, Université Pierre et Marie Curie - Paris VI, 2011. http://tel.archives-ouvertes.fr/tel-00844394.
Full textHari, Lysianne. "Propagation non-linéaire de paquets d'onde." Thesis, Cergy-Pontoise, 2014. http://www.theses.fr/2014CERG0726/document.
Full textThis thesis is devoted to the study of coupled nonlinear Schrödinger equations in the semi-classical limit.Depending on the potential we consider, the system can present a linear coupling, in addition to the nonlinear one.We will focus on the propagation of coherent states that will be polarized along a given eigenvector of the potential.In the linear setting, several situations have been analyzed; some of them lead to adiabatic theorems whereas the others implytransitions between energy levels. When one adds a nonlinearity, understanding nonlinear effects onthe propagation and the competition between them and the linear coupling becomes a very interesting issue.We first consider a potential with eigenvalues that present a spectral gap and will prove an adiabatic theoremfor a critical nonlinearity in the semi-classical sense. This is a L^2-supercritical result,similar to the one proved by Carles and Fermanian-Kammerer for the one-dimensional case, which is L^2-subcritical.The second part of the thesis deals with an explicit 2 X 2 potential that presents an avoided crossing point :the minimal gap between its eigenvalues becomes smaller as the semiclassical parameter tends to zero. We will prove that this system exhibits transitions between the modes. This result is a nonlinear version of the study performed by Hagedorn and Joye in the linear case
Achache, Mahdi. "Maximal regularity for non-autonomous evolution equations." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0026/document.
Full textThis Thesis is devoted to certain properties of non-autonomous evolution equations $u'(t)+A(t)u(t)=f(t), u(0)=x.$ More precisely, we are interested in the maximal $L^p$-regularity: given $fin L^{p}(0,tau;H),$ prove existence and uniqueness of the solution $u in W^{1,p}(0,tau;H)$. This problem was intensively studied in the autonomous cas, i.e., $A(t)=A$ for all $t.$ In the non-autonomous cas, the problem was considered by J.L.Lions in 1960. We prove serval results which extend all previously known ones on this problem. Here we assume that the familly of the operators $(mathcal{A}(t))_{tin [0,tau]}$ is associated with quasi-coercive, non-autonomous forms $(fra(t))_{t in [0,tau]}.$ We also consider the problem of maximal regularity for second order equations (the wave equation). Serval examples and applications are given in this Thesis
Chen, Hua, and Tahara Hidetoshi. "On the holomorphic solution of non-linear totally characteristic equations." Universität Potsdam, 1998. http://opus.kobv.de/ubp/volltexte/2008/2533/.
Full textNascimento, Wanderley Nunes do. "Klein-Gordon models with non-effective time-dependent potential." Universidade Federal de São Carlos, 2016. https://repositorio.ufscar.br/handle/ufscar/7453.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
In this thesis we study the asymptotic properties for the solution of the Cauchy problem for the Klein-Gordon equation with non-effective time-dependent potential. The main goal was define a suitable energy related to the Cauchy problem and derive decay estimates for such energy. Strichartz’ estimates and results of scattering and modified scattering was established. The C m theory and the stabilization condition was applied to treat the case where the coefficient of the potential term has very fast oscillations. Moreover, we consider a semi-linear wave model scale-invariant time- dependent with mass and dissipation, in this step we used linear estimates related with the semi-linear model to prove global existence (in time) of energy solutions for small data and we show a blow-up result for a suitable choice of the coefficients.
Nesta tese estudamos as propriedades assintóticas para a solução do problema de Cauchy para a equação de Klein-Gordon com potencial não efetivo dependente do tempo. O principal objetivo foi definir uma energia adequada relacionada ao problema de Cauchy e derivar estimativas para tal energia. Estimativas de Strichartz e resultados de scatering e scatering modificados também foram estabelecidos. A teoria C m e a condição de estabilização foram aplicados para tratar o caso em que o coeficiente da massa oscila muito rápido. Além disso, consideramos um mod- elo de onda semi-linear scale-invariante com massa e dissipação dependentes do tempo, nesta etapa usamos as estimativas lineares de tal modelo para provar ex- istência global (no tempo) de solução de energia para dados iniciais suficientemente pequenos e demonstramos um resultado de blow-up para uma escolha adequada dos coeficientes.
Tkachov, Pasha [Verfasser], and Oleksandr [Akademischer Betreuer] Kutovyi. "Front propagation in the non-local Fisher-KPP equation / Pasha Tkachov ; Betreuer: Oleksandr Kutovyi." Bielefeld : Universitätsbibliothek Bielefeld, 2017. http://d-nb.info/1135724598/34.
Full textKuang, Shilong. "Analysis of conjugate heat equation on complete non-compact Riemannian manifolds under Ricci flow." Diss., UC access only, 2009. http://proquest.umi.com/pqdweb?index=7&did=1907270831&SrchMode=2&sid=2&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1270053784&clientId=48051.
Full textIncludes abstract. Includes bibliographical references (leaves 74-76). Issued in print and online. Available via ProQuest Digital Dissertations.