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Stochastic Quasilinear Parabolic Equations With Non Standard Growth
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Book Synopsis Stochastic Quasilinear Parabolic Equations with Non Standard Growth by : Ali Zakaria Idriss
Download or read book Stochastic Quasilinear Parabolic Equations with Non Standard Growth written by Ali Zakaria Idriss and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis consists of two main parts. The rst part concerns the existence of weak probabilistic solutions (called elsewhere martingale solutions) for a stochastic quasilinear parabolic equation of generalized polytropic ltration, characterized by the presence of a nonlinear elliptic part admitting nonstandard growth. The deterministic version of the equation was rst introduced and studied by Samokhin in [178] as a generalized model for polytropic ltration. Our objective is to investigate the corresponding stochastic counterpart in the functional setting of generalized Lebesgue and Sobolev spaces. We establish an existence result of weak probabilistic solutions when the forcing terms do not satisfy Lipschitz conditions and the noise involves cylindrical Wiener processes. The second part is devoted to the existence and uniqueness results for a class of strongly nonlinear stochastic parabolic partial di erential equations. This part aims to treat an important class of higher-order stochastic quasilinear parabolic equations involving unbounded perturbation of zeroth order. The deterministic case was studied by Brezis and Browder (Proc. Natl. Acad. Sci. USA, 76(1): 38-40, 1979). Our main goal is to provide a detailed study of the corresponding stochastic problem. We establish the existence of a probabilistic weak solution and a unique strong probabilistic solution. The main tools used in this part of the thesis are a regularization through a truncation procedure which enables us to adapt the work of Krylov and Rozosvkii (Journal of Soviet Mathematics, 14: 1233-1277, 1981), combined with analytic and probabilistic compactness results (Prokhorov and Skorokhod Theorems), the theory of pseudomonotone operators, and a Banach space version of Yamada-Watanabe's theorem due to R ockner, Schmuland and Zhang. The study undertaken in this thesis is in some sense pioneering since both classes of stochastic partial di erential equations have not been the object of previous investigation, to the best of our knowledge. The results obtained are therefore original and constitute in our view signi cant contribution to the nonlinear theory of stochastic parabolic equations.
Book Synopsis Existence Result for a Class of Stochastic Quasilinear Partial Differential Equations with Non-standard Growth by : Zakaria Idriss Ali
Download or read book Existence Result for a Class of Stochastic Quasilinear Partial Differential Equations with Non-standard Growth written by Zakaria Idriss Ali and published by . This book was released on 2010 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Parabolic Equations with Irregular Data and Related Issues by : Claude Le Bris
Download or read book Parabolic Equations with Irregular Data and Related Issues written by Claude Le Bris and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-06-17 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the existence and uniqueness of solutions to parabolic-type equations with irregular coefficients and/or initial conditions. It elaborates on the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations, and also examines the connection between the results on the partial differential equation and the well-posedness of the underlying stochastic/ordinary differential equation.
Book Synopsis Potential Estimates and Quasilinear Parabolic Equations with Measure Data by : Quoc-Hung Nguyen
Download or read book Potential Estimates and Quasilinear Parabolic Equations with Measure Data written by Quoc-Hung Nguyen and published by American Mathematical Society. This book was released on 2024-01-19 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis A Regularity Result for Quasilinear Stochastic Partial Differential Equations of Parabolic Type by : Arnaud Debussche
Download or read book A Regularity Result for Quasilinear Stochastic Partial Differential Equations of Parabolic Type written by Arnaud Debussche and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Growth of Solutions of Quasi-Linear Parabolic Equations (Classic Reprint) by : Stanley Kaplan
Download or read book On the Growth of Solutions of Quasi-Linear Parabolic Equations (Classic Reprint) written by Stanley Kaplan and published by Forgotten Books. This book was released on 2018-02-09 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from On the Growth of Solutions of Quasi-Linear Parabolic Equations In fact, we might alternately have entitled this work What one may say about quasi-linear parabolic equations without using anything deep like Greens' functions, Schauder estimates, or Nash's theorem. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Book Synopsis Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications by : Victor A. Galaktionov
Download or read book Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications written by Victor A. Galaktionov and published by CRC Press. This book was released on 2004-05-24 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by Plya in the 1930's and rediscovered in part several times since, it was not un
Book Synopsis Regularity Theory and Stochastic Flows for Parabolic \ISPDES\n by : Franco Flandoli
Download or read book Regularity Theory and Stochastic Flows for Parabolic \ISPDES\n written by Franco Flandoli and published by CRC Press. This book was released on 1995-08-03 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1995. Routledge is an imprint of Taylor & Francis, an informa company.
Book Synopsis Qualitative Theory of Parabolic Equations, Part 1 by : T. I. Zelenyak
Download or read book Qualitative Theory of Parabolic Equations, Part 1 written by T. I. Zelenyak and published by Walter de Gruyter. This book was released on 2011-09-06 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the qualitative theory of ordinary differential equations, the Liapunov method plays a fundamental role. To use their analogs for the analysis of stability of solutions to parabolic, hyperparabolic, and other nonclassical equations and systems, time-invariant a priori estimates have to be devised for solutions. In this publication only parabolic problems are considered. Here lie, mainly, the problems which have been investigated most thoroughly --- the construction of Liapunov functionals which naturally generalize Liapunov functions for nonlinear parabolic equations of the second order with one spatial variable. The authors establish stabilizing solutions theorems, and the necessary and sufficient conditions of general and asymptotic stability of stationary solutions, including the so-called critical case. Attraction domains for stable solutions of mixed problems for these equations are described. Furthermore, estimates for the number of stationary solutions are obtained.
Book Synopsis Backward Stochastic Differential Equations by : N El Karoui
Download or read book Backward Stochastic Differential Equations written by N El Karoui and published by CRC Press. This book was released on 1997-01-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.
Book Synopsis Blow-up Theories for Semilinear Parabolic Equations by : Bei Hu
Download or read book Blow-up Theories for Semilinear Parabolic Equations written by Bei Hu and published by Springer Science & Business Media. This book was released on 2011-03-23 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.
Book Synopsis Stochastic Partial Differential Equations, Second Edition by : Pao-Liu Chow
Download or read book Stochastic Partial Differential Equations, Second Edition written by Pao-Liu Chow and published by CRC Press. This book was released on 2014-12-10 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore Theory and Techniques to Solve Physical, Biological, and Financial Problems Since the first edition was published, there has been a surge of interest in stochastic partial differential equations (PDEs) driven by the Lévy type of noise. Stochastic Partial Differential Equations, Second Edition incorporates these recent developments and improves the presentation of material. New to the Second Edition Two sections on the Lévy type of stochastic integrals and the related stochastic differential equations in finite dimensions Discussions of Poisson random fields and related stochastic integrals, the solution of a stochastic heat equation with Poisson noise, and mild solutions to linear and nonlinear parabolic equations with Poisson noises Two sections on linear and semilinear wave equations driven by the Poisson type of noises Treatment of the Poisson stochastic integral in a Hilbert space and mild solutions of stochastic evolutions with Poisson noises Revised proofs and new theorems, such as explosive solutions of stochastic reaction diffusion equations Additional applications of stochastic PDEs to population biology and finance Updated section on parabolic equations and related elliptic problems in Gauss–Sobolev spaces The book covers basic theory as well as computational and analytical techniques to solve physical, biological, and financial problems. It first presents classical concrete problems before proceeding to a unified theory of stochastic evolution equations and describing applications, such as turbulence in fluid dynamics, a spatial population growth model in a random environment, and a stochastic model in bond market theory. The author also explores the connection of stochastic PDEs to infinite-dimensional stochastic analysis.
Book Synopsis Local Behavior of Solutions of Quasilinear Parabolic Equations by : Richard Allen Hager
Download or read book Local Behavior of Solutions of Quasilinear Parabolic Equations written by Richard Allen Hager and published by . This book was released on 1967 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :University of Minnesota. Institute for Mathematics and Its Applications Publisher : ISBN 13 : Total Pages :23 pages Book Rating :4.:/5 (123 download)
Book Synopsis Optimal Control of Quasilinear Parabolic Equations by : University of Minnesota. Institute for Mathematics and Its Applications
Download or read book Optimal Control of Quasilinear Parabolic Equations written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1993 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Solution of a Class of Quasilinear Parabolic Equations by : James G. Berryman
Download or read book Solution of a Class of Quasilinear Parabolic Equations written by James G. Berryman and published by . This book was released on 1976 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Smooth Solutions of Systems of Quasilinear Parabolic Equations by : Alain Bensoussan
Download or read book Smooth Solutions of Systems of Quasilinear Parabolic Equations written by Alain Bensoussan and published by . This book was released on 2001 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Global Solutions and Equilibrium States of Quasilinear Parabolic Equations by : Wu-teh Hsiang
Download or read book Global Solutions and Equilibrium States of Quasilinear Parabolic Equations written by Wu-teh Hsiang and published by . This book was released on 1977 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
