Relevant bibliographies by topics / Parabolic evolution equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Parabolic evolution equation'

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Published: 11 March 2023

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Journal articles on the topic "Parabolic evolution equation"

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Kranysˇ, M. "Causal Theories of Evolution and Wave Propagation in Mathematical Physics." Applied Mechanics Reviews 42, no. 11 (November 1, 1989): 305–22. http://dx.doi.org/10.1115/1.3152415.

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There are still many phenomena, especially in continuum physics, that are described by means of parabolic partial differential equations whose solution are not compatible with the causality principle. Compatibility with this principle is required also by the theory of relativity. A general form of hyperbolic operators for the most frequently occurring linear governing equations in mathematical physics is written down. It is then easy to convert any given parabolic equation to the hyperbolic form without necessarily entering into the cause of the inadequacy of the governing equation. The method is verified on the well-known example of Timoshenko’s correction of the Bernoulli–Euler–Rayleigh beam equation for flexural motion. The “Love–Rayleigh” fourth-order differential equations for the longitudinal and torsional wave propagation in the rod is generalized with this method. The hyperbolic version (not to mention others) of the linear Korteweg–de Vries equation and of the “telegraph” equation governing electromagnetic wave propagation through relaxing material are given. Lagrangians of all the equations studied are listed. For all the reasons given we believe the hyperbolic governing equations to be physically and mathematically more realistic and adequate.
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Ashyralyev, Allaberen, Yasar Sozen, and Fatih Hezenci. "A note on evolution equation on manifold." Filomat 35, no. 15 (2021): 5031–43. http://dx.doi.org/10.2298/fil2115031a.

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In the present paper, considering the differential equations on smooth closed manifolds, we investigate and establish the well-posedness of boundary value problems nonlocal type for parabolic equations and also hyperbolic equations in H?lder spaces. Furthermore, in various H?lder norms we establish new coercivity estimates for the solutions of such type parabolic boundary value problems on manifolds and hyperbolic boundary value problems on manifolds as well.
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Avalishvili, Gia, and Mariam Avalishvili. "On nonclassical problems for first-order evolution equations." gmj 18, no. 3 (July 14, 2011): 441–63. http://dx.doi.org/10.1515/gmj.2011.0028.

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Abstract The present paper deals with nonclassical initial-boundary value problems for parabolic equations and systems and their generalizations in abstract spaces. Nonclassical problems with nonlocal initial conditions for an abstract first-order evolution equation with time-dependent operator are considered, the existence and uniqueness results are proved and the algorithm of approximation of nonlocal problems by a sequence of classical problems is constructed. Applications of the obtained general results to initial-boundary value problems for parabolic equations and systems are considered.
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Colli, Pierluigi, Gianni Gilardi, and Jürgen Sprekels. "Constrained Evolution for a Quasilinear Parabolic Equation." Journal of Optimization Theory and Applications 170, no. 3 (July 6, 2016): 713–34. http://dx.doi.org/10.1007/s10957-016-0970-6.

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Vidossich, Giovanni. "Solving Becker’s Problem on Periodic Solutions of Parabolic Evolution Equations." Advanced Nonlinear Studies 18, no. 2 (April 1, 2018): 195–215. http://dx.doi.org/10.1515/ans-2017-6047.

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Abstract We present existence and multiplicity theorems for periodic mild solutions to parabolic evolution equations. Their peculiarity is a link with the spectrum of the generator of the semigroup rather than with the spectrum of the linearized periodic BVP for the evolution equation. They provide a positive solution to the open problem risen by Becker [3], they extend some results of Castro and Lazer [5] from scalar to systems of parabolic equations, and they are new even for finite-dimensional ODEs.
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LIN, CHIN-YUAN. "SOME NON-DISSIPATIVITY CONDITION FOR EVOLUTION EQUATIONS." International Journal of Mathematics 24, no. 02 (February 2013): 1350002. http://dx.doi.org/10.1142/s0129167x1350002x.

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Of concern is the nonlinear evolution equation [Formula: see text] in a real Banach space X, where the nonlinear, time-dependent, multi-valued operator [Formula: see text] has a time-dependent domain D(A(t)). It will be shown that, under some non-dissipativity condition, the equation has a strong solution. Illustrations are given of solving quasi-linear partial differential equations of parabolic type.
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Karachalios, Nikos, Nikos Stavrakakis, and Pavlos Xanthopoulos. "Asymptotic behavior of solutions for a semibounded nonmonotone evolution equation." Abstract and Applied Analysis 2003, no. 9 (2003): 521–38. http://dx.doi.org/10.1155/s1085337503210022.

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We consider a nonlinear parabolic equation involving nonmonotone diffusion. Existence and uniqueness of solutions are obtained, employing methods for semibounded evolution equations. Also shown is the existence of a global attractor for the corresponding dynamical system.
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Motsa, S. S., V. M. Magagula, and P. Sibanda. "A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations." Scientific World Journal 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/581987.

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This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
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Su, Ning, and Li Zhang. "Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/567241.

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We consider an abstract Cauchy problem for a doubly nonlinear evolution equation of the formd/dt𝒜u+ℬu∋ftinV′,t∈0, T, whereVis a real reflexive Banach space,𝒜andℬare maximal monotone operators (possibly multivalued) fromVto its dualV′. In view of some practical applications, we assume that𝒜andℬare subdifferentials. By using the back difference approximation, existence is established, and our proof relies on the continuity of𝒜and the coerciveness ofℬ. As an application, we give the existence for a nonlinear degenerate parabolic equation.
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Bulíček, Miroslav, Piotr Gwiazda, Endre Süli, and Agnieszka Świerczewska-Gwiazda. "Analysis of a viscosity model for concentrated polymers." Mathematical Models and Methods in Applied Sciences 26, no. 08 (June 7, 2016): 1599–648. http://dx.doi.org/10.1142/s0218202516500391.

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The paper is concerned with a class of mathematical models for polymeric fluids, which involves the coupling of the Navier–Stokes equations for a viscous, incompressible, constant-density fluid with a parabolic–hyperbolic integro-differential equation describing the evolution of the polymer distribution function in the solvent, and a parabolic integro-differential equation for the evolution of the monomer density function in the solvent. The viscosity coefficient, appearing in the balance of linear momentum equation in the Navier–Stokes system, includes dependence on the shear rate as well as on the weight-averaged polymer chain length. The system of partial differential equations under consideration captures the impact of polymerization and depolymerization effects on the viscosity of the fluid. We prove the existence of global-in-time, large-data weak solutions under fairly general hypotheses.
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Dissertations / Theses on the topic "Parabolic evolution equation"

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URBANI, CRISTINA. "Bilinear Control of Evolution Equations." Doctoral thesis, Gran Sasso Science Institute, 2020. http://hdl.handle.net/20.500.12571/10061.

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The thesis is devoted to the study of the stabilization and the controllability of the evolution equations $$u'(t) + Au (t) + p (t) Bu (t) = 0$$ by means of a bilinear control $p$. Bilinear controls are coefficients of the equation that multiply the state variable. Multiplicative controls are therefore suitable to describe processes that change their principal parameters in presence of a control. We first present a result of rapid stabilization of the parabolic equations towards the ground state by bilinear control with a doubly exponential rate of convergence. Under stronger hypotheses on the potential $B$, we show results of exact local and global controllability towards the solution of the ground state in arbitrarily small time. We apply these two abstract results to different types of PDE such as the heat equation, or parabolic equations with non-constant coefficients. We then prove local exact controllability of a class of degenerate wave equations relying on a sharp analysis of the spectral properties of the elliptic degenerate operators. We then present a method of constructing multiplicative operators $B$ verifying the sufficient hypotheses required for controllability or stabilization results. This method leads to constructive algorithms of infinite explicit families of such operators $B$. We then prove new controllability results for the Schr{"o}dinger equation with hybrid boundary conditions. We also give applications of our method to parabolic equations leading to results of rapid stabilization, local and global controllability to the ground state which are explicit with respect to the operators $B$.
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Achache, Mahdi. "Maximal regularity for non-autonomous evolution equations." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0026/document.

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Cette thèse est dédiée a l''etude de certaines propriétés des équations d' évolutions non-autonomes $u'(t)+A(t)u(t)=f(t), u(0)=x.$ Il s'agit précisément de la propriété de la régularité maximale $L^p$: étant donnée $fin L^{p}(0,tau;H)$, montrer l'existence et unicité de la solution $u in W^{1,p}(0,tau;H)$. Ce problème a 'et'e intensivement étudie dans le cas autonome, i.e., $A(t)=A$ pour tout $t$. Dans le cas non-autonome, le problème a été considéré par J.L.Lions en 1960. Nous montrons divers résultats qui étendent tout ce qui est connu sur ce problème. On suppose ici que la famille des opérateurs $(mathcal{A}(t))_{tin [0,tau]}$ est associée à des formes quasi-coercives, non autonomes $(fra(t))_{t in [0,tau]}.$ Nous considérons également le problème de régularité maximale pour les d'ordre 2 (équations des ondes). Plusieurs exemples et applications sont considérés
This 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
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ALESSANDRONI, ROBERTA. "Evolution of hypersurfaces by curvature functions." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2008. http://hdl.handle.net/2108/661.

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Consideriamo un'ipersuperficie liscia di ℝⁿ⁺¹, con n≥2, e la sua evoluzione secondo una classe di flussi geometrici. La velocità di questi flussi ha direzione normale alla superficie e il modulo è una funzione simmetrica delle curvature principali. Inizialmente mostriamo alcune proprietà generali di questi flussi e calcoliamo l'equazione di evoluzione per una generica funzione omogenea delle curvature principali. In particolare applichiamo il flusso con velocità S=(H/(logH)), dove H è la curvatura media a meno di una costante, ad una superficie con curvatura media positiva per ottenere delle stime di convessità. Usando solamente il principio del massimo dimostriamo che, su un limite di riscalamenti delle superfici che si evolvono vicino alla singolarità, la parte negativa della curvatura scalare tende a zero. La parte successiva è dedicata allo studio di un'ipersuperficie convessa che si evolve secondo potenze della curvatura scalare: S=R^{p}, con p>1/2. Si dimostra che se la superficie iniziale soddisfa delle stime di "pinching" sulle curvature principali allora si contrae ad un punto in tempo finito e la forma delle superfici che si evolvono approssima sempre più quella di una sfera. In questo caso il grado di omogeneità, strettamente maggiore di uno, permette di concludere la dimostrazione della convergenza ad un "punto rotondo" tramite il solo principio del massimo, evitando l'uso di stime integrali. Viene anche costruito un esempio di superficie convessa che forma una singolarità di tipo "neck pinching". Infine studiamo il caso di un grafico intero su ℝⁿ con crescita al più lineare all'infinito e mostriamo che un grafico che si evolve secondo un qualsiasi flusso nella classe considerata rimane un grafico. Inoltre dimostriamo un risultato di esistenza per tempi lunghi per i flussi con velocità S=R^{p} con p≥1/2 e descriviamo delle soluzioni esplicite per grafici a simmetria di rotazione.
We consider a smooth n-dimensional hypersurface of ℝⁿ⁺¹, with n≥2, and its evolution by a class of geometric flows. The speed of these flows has normal direction with respect to the surface and its modulus S is a symmetric function of the principal curvatures. We show some general properties of these flows and compute the evolution equation for any homogeneous function of principal curvatures. Then we apply the flow with speed S=(H/(logH)), where H is the mean curvature plus a constant, to a mean convex surface to prove some convexity estimates. Using only the maximum principle we prove that the negative part of the scalar curvature tends to zero on a limit of rescalings of the evolving surfaces near a singularity. The following part is dedicated to the study of a convex initial manifold moving by powers of scalar curvature: S=R^{p}, with p>1/2. We show that if the initial surface satisfies a pinching estimate on the principal curvatures then it shrinks to a point in finite time and the shape of the evolving surfaces approaches the one of a sphere. Since the homogeneity degree of this speed is strictly greater than one, the convergence to a "round point" can be proved using just the maximum principle, avoiding the integral estimates. Then we also construct an example of a non convex surface forming a neck pinching singularity. Finally we study the case of an entire graph over ℝⁿ with at most linear growth at infinity. We show that a graph evolving by any flow in the considered class remains a graph. Moreover we prove a long time existence result for flows where the speed is S=R^{p} with p≥1/2 and describe some explicit solutions in the rotationally symmetric case.
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Ta, Thi nguyet nga. "Sub-gradient diffusion equations." Thesis, Limoges, 2015. http://www.theses.fr/2015LIMO0137/document.

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Ce mémoire de thèse est consacrée à l'étude des problèmes d'évolution où la dynamique est régi par l'opérateur de diffusion de sous-gradient. Nous nous intéressons à deux types de problèmes d'évolution. Le premier problème est régi par un opérateur local de type Leray-Lions avec un domaine borné. Dans ce problème, l'opérateur est maximal monotone et ne satisfait pas la condition standard de contrôle de la croissance polynomiale. Des exemples typiques apparaît dans l'étude de fluide non-Neutonian et aussi dans la description de la dynamique du flux de sous-gradient. Pour étudier le problème nous traitons l'équation dans le contexte de l'EDP non linéaire avec le flux singulier. Nous utilisons la théorie de gradient tangentiel pour caractériser l'équation d'état qui donne la relation entre le flux et le gradient de la solution. Dans le problème stationnaire, nous avons l'existence de la solution, nous avons également l'équivalence entre le problème minimisation initial, le problème dual et l'EDP. Dans l'équation de l'évolution, nous proposons l'existence, l'unicité de la solution. Le deuxième problème est régi par un opérateur discret. Nous étudions l'équation d'évolution discrète qui décrivent le processus d'effondrement du tas de sable. Ceci est un exemple typique de phénomènes auto-organisés critiques exposées par une slope critique. Nous considérons l'équation d'évolution discrète où la dynamique est régie par sous-gradient de la fonction d'indicateur de la boule unité. Nous commençons par établir le modèle, nous prouvons existence et l'unicité de la solution. Ensuite, en utilisant arguments de dualité nous étudions le calcul numérique de la solution et nous présentons quelques simulations numériques
This thesis is devoted to the study of evolution problems where the dynamic is governed by sub-gradient diffusion operator. We are interest in two kind of evolution problems. The first problem is governed by local operator of Leray-Lions type with a bounded domain. In this problem, the operator is maximal monotone and does not satisfied the standard polynomial growth control condition. Typical examples appears in the study of non-Neutonian fluid and also in the description of sub-gradient flows dynamics. To study the problem we handle the equation in the context of nonlinear PDE with singular flux. We use the theory of tangential gradient to characterize the state equation that gives the connection between the flux and the gradient of the solution. In the stationary problem, we have the existence of solution, we also get the equivalence between the initial minimization problem, the dual problem and the PDE. In the evolution one, we provide the existence, uniqueness of solution and the contractions. The second problem is governed by a discrete operator. We study the discrete evolution equation which describe the process of collapsing sandpile. This is a typical example of Self-organized critical phenomena exhibited by a critical slop. We consider the discrete evolution equation where the dynamic is governed by sub-gradient of indicator function of the unit ball. We begin by establish the model, we prove existence and uniqueness of the solution. Then by using dual arguments we study the numerical computation of the solution and we present some numerical simulations
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Döding, Christian [Verfasser]. "Stability of Traveling Oscillating Fronts in Parabolic Evolution Equations / Christian Döding." Bielefeld : Universitätsbibliothek Bielefeld, 2019. http://d-nb.info/1191896382/34.

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Portal, Pierre. "Harmonic analysis of banach space valued functions in the study of parabolic evolution equations /." free to MU campus, to others for purchase, 2004. http://wwwlib.umi.com/cr/mo/fullcit?p3137737.

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Bredies, Kristian. "Optimal control of degenerate parabolic equations in image processing : analysis of evolution equations with variable degeneracy and associated minimization problems /." Berlin : Logos-Verl, 2008. http://deposit.d-nb.de/cgi-bin/dokserv?id=3071675&prov=M&dok_var=1&dok_ext=htm.

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Bredies, Kristian. "Optimal control of degenerate parabolic equations in image processing analysis of evolution equations with variable degeneracy and associated minimization problems." Berlin Logos-Verl, 2007. http://d-nb.info/987598511/04.

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Johnsen, Pernilla. "Homogenization of Partial Differential Equations using Multiscale Convergence Methods." Licentiate thesis, Mittuniversitetet, Institutionen för matematik och ämnesdidaktik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-42036.

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The focus of this thesis is the theory of periodic homogenization of partial differential equations and some applicable concepts of convergence. More precisely, we study parabolic problems exhibiting both spatial and temporal microscopic oscillations and a vanishing volumetric heat capacity type of coefficient. We also consider a hyperbolic-parabolic problem with two spatial microscopic scales. The tools used are evolution settings of multiscale and very weak multiscale convergence, which are extensions of, or closely related to, the classical method of two-scale convergence. The novelty of the research in the thesis is the homogenization results and, for the studied parabolic problems, adapted compactness results of multiscale convergence type.
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Wolf, Jörg. "Regularität schwacher Lösungen nichtlinearer elliptischer und parabolischer Systeme partieller Differentialgleichungen mit Entartung." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2002. http://dx.doi.org/10.18452/14792.

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In der vorliegenden Arbeit untersuchen wir schwache Lösungen, die zu einem geeigneten Sobolevraum gehören, q-elliptischer und parabolischer Systeme partieller Differentialgleichungen auf deren Regularität für den Fall 1
In the present work we study the regularity of weak solution to q-elliptic and parabolic systems partial differential equations in appropriate Sobolev spaces in case 1
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Books on the topic "Parabolic evolution equation"

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Bejenaru, Ioan. Near soliton evolution for equivariant Schrödinger maps in two spatial dimensions. Providence, Rhode Island: American Mathematical Society, 2013.

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Prüss, Jan, and Gieri Simonett. Moving Interfaces and Quasilinear Parabolic Evolution Equations. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-27698-4.

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Yagi, Atsushi. Abstract Parabolic Evolution Equations and their Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-04631-5.

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Linear and quasilinear parabolic problems. Basel: Birkhäuser Verlag, 1995.

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Daners, D. Abstract evolution equations, periodic problems and applications. Essex, England: Longman Scientific & Technical, 1992.

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Yagi, Atsushi. Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality II. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-2663-0.

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Yagi, Atsushi. Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-1896-3.

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Engquist, Bjorn. Fast wavelet based algorithms for linear evolution equations. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1992.

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Surface evolution equations: A level set approach. Boston: Birkhäuser Verlag, 2006.

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1963-, Ruan Shigui, ed. Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models. Providence, R.I: American Mathematical Society, 2009.

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Book chapters on the topic "Parabolic evolution equation"

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Desch, Wolfgang, and Stig-Olof Londen. "On a Stochastic Parabolic Integral Equation." In Functional Analysis and Evolution Equations, 157–69. Basel: Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-7794-6_10.

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Diop, Mamadou Abdoul, and Etienne Pardoux. "Averaging of a Parabolic Partial Differential Equation with Random Evolution." In Seminar on Stochastic Analysis, Random Fields and Applications IV, 111–28. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7943-9_8.

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Prüss, Jan, and Gieri Simonett. "Quasilinear Parabolic Evolution Equations." In Moving Interfaces and Quasilinear Parabolic Evolution Equations, 195–230. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-27698-4_5.

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Rozovskii, B. L. "Ito’s Second Order Parabolic Equations." In Stochastic Evolution Systems, 125–74. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-011-3830-7_4.

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Rozovsky, Boris L., and Sergey V. Lototsky. "Itô’s Second-Order Parabolic Equations." In Stochastic Evolution Systems, 123–70. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94893-5_4.

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Cherrier, Pascal, and Albert Milani. "The Parabolic Case." In Evolution Equations of von Karman Type, 101–23. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20997-5_5.

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Prüss, Jan, and Gieri Simonett. "Further Parabolic Evolution Problems." In Moving Interfaces and Quasilinear Parabolic Evolution Equations, 515–70. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-27698-4_12.

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Saichev, Alexander I., and Wojbor A. Woyczyński. "Diffusions and Parabolic Evolution Equations." In Distributions in the Physical and Engineering Sciences, Volume 2, 59–91. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-0-8176-4652-3_2.

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Rozovskii, B. L. "Hypoellipticity of Ito’s Second Order Parabolic Equations." In Stochastic Evolution Systems, 251–93. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-011-3830-7_7.

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Rozovsky, Boris L., and Sergey V. Lototsky. "Hypoellipticity of Itô’s Second Order Parabolic Equations." In Stochastic Evolution Systems, 243–78. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94893-5_7.

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Conference papers on the topic "Parabolic evolution equation"

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Leftheriotis, Georgios A., and Athanassios A. Dimas. "Coupled Simulation of Oscillatory Flow, Sediment Transport and Morphology Evolution of Ripples Based on the Immersed Boundary Method." In ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/omae2014-24006.

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In the present study, numerical simulations of oscillatory flow over a rippled bottom, coupled with bed and suspended sediment transport, as well as the resulting morphology evolution, are performed. The simulations are based on the numerical solution of the Navier-Stokes equations and the advection-diffusion equation for the suspended load, while empirical formulas are used for the bed load. The bed morphological evolution is obtained by the numerical solution of the conservation of sediment mass equation. A fractional time-step scheme is used for the temporal discretization, while finite differences are used for the spatial discretization on a Cartesian grid. The Immersed Boundary method is implemented for the imposition of fluid and sediment boundary conditions on the ripple surface. Two types of ripples are examined, i.e., ripples of parabolic shape with sharp crests and sinusoidal ripples, and cases of ripple length to orbital motion amplitude ratio of 1.6 and ripple height to orbital motion amplitude ratios of 0.16, 0.20 and 0.24, at Reynolds number equal to 5×103. The effect of ripple steepness and ripple shape on suspended sediment and ripple migration is discussed.
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Lee, Jung Lyul, and John Rong-Chung Hsu. "Numerical Simulation of Dynamic Shoreline Changes Behind a Detached Breakwater by Using an Equilibrium Formula." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-62622.

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Salient and tombolo are common features found in the lee of detached breakwaters. The empirical parabolic bay shape equation (PBSE) can be applied when their planform is fully developed, whereas numerical model is required to simulate the dynamic shoreline evolution prior to the planform reaching static equilibrium. This paper reports the excellent performance of PBSE through the comparison with labaratory results and the development of a numerical model for dynamic shoreline change that utilizes the concept of PBSE and equilibrium beach profile. Formulation proposed for sediment transport rate is theoretically compared with that in GENESIS. The governing equation for the combined shoreline response model is based on the one-line beach model, which includes shoreline changes owing to longshore and cross-shore sediment transport. Finally, numerical results reveal, by comparing with an experimental case in the laboratory, that the model is adequate to successively simulating the dynamic evolutions of the shoreline behind a detached breakwater.
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3

Caruntu, Dumitru I. "On Superharmonic Resonances of Nonlinear Nonuniform Beams." In ASME 2008 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2008. http://dx.doi.org/10.1115/smasis2008-599.

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Superharmonic resonances of nonlinear forced bending vibrations of moderately large curvature of nonuniform cantilever beams of rectangular cross section and a sharp end are reported. Cantilevers of constant width and parabolic thickness variation are considered in this paper. Method of multiple scales is directly applied to the governing partial-differential equation of motion and boundary conditions. Two problems, zero- and first-order problem, result. Solving the zero-order problem, the linear modes are obtained in terms of hypergeometric functions by using the factorization method. The first-order problem provides the amplitude and phase evolution equation and consequently the superharmonic frequency response of the nonlinear system.
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4

Caruntu, Dumitru I. "On Subharmonic Resonances of Geometric Nonlinear Vibrations of Nonuniform Beams." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-67727.

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Subharmonic resonances of nonlinear forced bending vibrations in the case of moderately large curvature of nonuniform cantilever beams of rectangular cross section and a sharp end are reported. Cantilevers of constant width and parabolic thickness variation are considered in this research. The method of multiple scales is directly applied to the governing partial-differential equation of motion and boundary conditions. Two problems, zeroth- and first-order, result. Using factorization method, the linear modes of the zeroth-order problem are obtained in terms of hypergeometric functions. The first-order problem provides the amplitude and phase evolution equation and consequently the regions where subharmonic responses exist.
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5

Caruntu, Dumitru I. "Simultaneous Resonances of Geometric Nonlinear Nonuniform Beams." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86779.

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Simultaneous resonances, superharmonic and subharmonic, of two-term excitation nonlinear bending vibrations in the case of moderately large curvature of nonuniform cantilever beams are reported. Cantilevers of constant width and parabolic thickness variation are considered in this research. The method of multiple scales is directly applied to the governing partial-differential equation of motion and boundary conditions. Two problems, zero- and first-order, result. Using factorization method, the linear modes of the zero-order problem are obtained in terms of hypergeometric functions. The first-order problem provides the amplitude-phase evolution relationship and consequently the simultaneous resonances response.
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6

Kano, Risei, Yusuke Murase, and Nobuyuki Kenmochi. "Nonlinear evolution equations generated by subdifferentials with nonlocal constraints." In Nonlocal and Abstract Parabolic Equations and their Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc86-0-11.

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7

Chen, Minli, Changyuan Gao, Guoliang Zhang, Lin Shi, Liutao Chen, and Jun Tan. "Oxidation Behaviour of CZ Alloys Under High Temperature Steam." In 2022 29th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/icone29-93795.

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Abstract CZ Alloys, including CZ1 and CZ2, are new advanced zirconium alloys developed by China General Nuclear Power Group. This paper presents the oxidation behaviour of CZ Alloys and Zircaloy-4 in flowing steam. A SETSYS Evolution TGA (ThermoGravimetric Analyzer) is used for the high temperature testing. The weight gain of specimens was measured real time in the temperature range of 800∼1200 °C for 3000∼5000s. The hydrogen content after oxidation at 1000 °C was measured. CZ1 (Zr-Sn-Nb alloy), CZ2 (Zr-Nb alloy) and Zircaloy-4 (Zr-Sn alloy) claddings which contain different types of alloying elements have similar oxidation behaviour at above 1100°C but show significant difference at lower temperatures. The weight gain of CZ Alloys are compared with high-temperature oxidation parabolic rate laws of fuel cladding materials which have been used in many LOCA analyses, the Baker-Just equation and the Carthcart-Pawel equation. The results show that the Baker-Just equation is conservative for CZ Alloys and the Carthcart-Pawel equation is more accurate at above 1100°C. The oxidation rate constant and the rate exponent are calculated at each temperature by non-linear fittings.
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Yamazaki, Noriaki. "Optimal control of nonlinear evolution equations associated with time-dependent subdifferentials and applications." In Nonlocal and Abstract Parabolic Equations and their Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc86-0-20.

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9

AMANN, HERBERT. "QUASILINEAR PARABOLIC FUNCTIONAL EVOLUTION EQUATIONS." In Proceedings of the 2004 Swiss-Japanese Seminar. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774170_0002.

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10

Cholewa, J. W., and T. Dłotko. "Bi-spaces global attractors in abstract parabolic equations." In Evolution Equations Propagation Phenomena - Global Existence - Influence of Non-Linearities. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc60-0-1.

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