Parabolic Equations
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Second Order Parabolic Differential Equations
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Author : Gary M. Lieberman
language : en
Publisher: World Scientific
Release Date : 1996
Second Order Parabolic Differential Equations written by Gary M. Lieberman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Introduction. Maximum principles. Introduction to the theory of weak solutions. Hölder estimates. Existence, uniqueness, and regularity of solutions. Further theory of weak solutions. Strong solutions. Fixed point theorems and their applications. Comparison and maximum principles. Boundary gradient estimates. Global and local gradient bounds. Hölder gradient estimates and existence theorems. The oblique derivative problem for quasilinear parabolic equations. Fully nonlinear equations. Introduction. Monge-Ampère and Hessian equations.
Degenerate Parabolic Equations
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Author : Emmanuele DiBenedetto
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Degenerate Parabolic Equations written by Emmanuele DiBenedetto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Evolved from the author's lectures at the University of Bonn's Institut für angewandte Mathematik, this book reviews recent progress toward understanding of the local structure of solutions of degenerate and singular parabolic partial differential equations.
Elliptic And Parabolic Equations
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Author : Zhuoqun Wu
language : en
Publisher: World Scientific Publishing Company
Release Date : 2006-10-17
Elliptic And Parabolic Equations written by Zhuoqun Wu and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-17 with Mathematics categories.
This book provides an introduction to elliptic and parabolic equations. While there are numerous monographs focusing separately on each kind of equations, there are very few books treating these two kinds of equations in combination. This book presents the related basic theories and methods to enable readers to appreciate the commonalities between these two kinds of equations as well as contrast the similarities and differences between them.
Parabolic Equations With Irregular Data And Related Issues
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Author : Claude Le Bris
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-06-17
Parabolic Equations With Irregular Data And Related Issues written by Claude Le Bris and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-17 with Mathematics categories.
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.
Parabolic Equations On An Infinite Strip
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Author : Watson
language : en
Publisher: Routledge
Release Date : 2017-10-02
Parabolic Equations On An Infinite Strip written by Watson and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-02 with Mathematics categories.
This book focuses on solutions of second order, linear, parabolic, partial differentialequations on an infinite strip-emphasizing their integral representation, their initialvalues in several senses, and the relations between these.Parabolic Equations on an Infinite Strip provides valuable information-previously unavailable in a single volume-on such topics as semigroup property.. . the Cauchy problem ... Gauss-Weierstrass representation . .. initial limits .. .normal limits and related representation theorems ... hyperplane conditions .. .determination of the initial measure .. . and the maximum principle. It also exploresnew, unpublished results on parabolic limits . . . more general limits ... and solutionssatisfying LP conditions.Requiring only a fundamental knowledge of general analysis and measure theory, thisbook serves as an excellent text for graduate students studying partial differentialequations and harmonic analysis, as well as a useful reference for analysts interested inapplied measure theory, and specialists in partial differential equations.
Partial Differential Equations Of Parabolic Type
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Author : Avner Friedman
language : en
Publisher: Courier Dover Publications
Release Date : 2008-04-21
Partial Differential Equations Of Parabolic Type written by Avner Friedman and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-21 with Mathematics categories.
With this book, even readers unfamiliar with the field can acquire sufficient background to understand research literature related to the theory of parabolic and elliptic equations. 1964 edition.
Blow Up Theories For Semilinear Parabolic Equations
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Author : Bei Hu
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-23
Blow Up Theories For Semilinear Parabolic Equations written by Bei Hu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-23 with Mathematics categories.
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.
Linear And Quasi Linear Equations Of Parabolic Type
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Author : Olʹga A. Ladyženskaja
language : en
Publisher: American Mathematical Soc.
Release Date : 1988
Linear And Quasi Linear Equations Of Parabolic Type written by Olʹga A. Ladyženskaja and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.
Qualitative Theory Of Parabolic Equations Part 1
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Author : T. I. Zelenyak
language : en
Publisher: Walter de Gruyter
Release Date : 2011-09-06
Qualitative Theory Of Parabolic Equations Part 1 written by T. I. Zelenyak and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-06 with Mathematics categories.
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.
Lectures On Elliptic And Parabolic Equations In Holder Spaces
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Author : Nikolaĭ Vladimirovich Krylov
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Lectures On Elliptic And Parabolic Equations In Holder Spaces written by Nikolaĭ Vladimirovich Krylov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in H older spaces. Krylov shows that this theory - including some issues of the theory of nonlinear equations - is based on some general and extremely powerful ideas and some simple computations. The main object of study is the first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative problems or problems involving higher-order elliptic operators acting on the boundary. Numerical approximations are also discussed. This book, containing 200 exercises, aims to provide a good understanding of what kind of results are available and what kinds of techniques are used to obtain them.