Nonlinear Second Order 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.

Nonlinear Elliptic And Parabolic Equations Of The Second Order

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Author : N.V. Krylov
language : en
Publisher: Springer
Release Date : 2001-11-30

Nonlinear Elliptic And Parabolic Equations Of The Second Order written by N.V. Krylov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-30 with Mathematics categories.

Approach your problems from the It isn't that they can't see the right end and begin with the solution. It is that they can't see answers. Then one day, perhaps the problem. you will find the final question. G.K. Chesterton. The Scandal of 'The Hermit Clad in Crane Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theor.etical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

Elliptic And Parabolic Equations With Discontinuous Coefficients

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Author : Antonino Maugeri
language : en
Publisher: Wiley-VCH
Release Date : 2000-12-13

Elliptic And Parabolic Equations With Discontinuous Coefficients written by Antonino Maugeri and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-12-13 with Mathematics categories.

This book unifies the different approaches in studying elliptic and parabolic partial differential equations with discontinuous coefficients. To the enlarging market of researchers in applied sciences, mathematics and physics, it gives concrete answers to questions suggested by non-linear models. Providing an up-to date survey on the results concerning elliptic and parabolic operators on a high level, the authors serve the reader in doing further research. Being themselves active researchers in the field, the authors describe both on the level of good examples and precise analysis, the crucial role played by such requirements on the coefficients as the Cordes condition, Campanato's nearness condition, and vanishing mean oscillation condition. They present the newest results on the basic boundary value problems for operators with VMO coefficients and non-linear operators with discontinuous coefficients and state a lot of open problems in the field.

Elliptic Parabolic Equations

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Author : Zhuoqun Wu
language : en
Publisher: World Scientific
Release Date : 2006

Elliptic Parabolic Equations written by Zhuoqun Wu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 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.

Nonlinear Second Order Parabolic Equations

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Author : Mingxin Wang
language : en
Publisher: CRC Press
Release Date : 2021-05-12

Nonlinear Second Order Parabolic Equations written by Mingxin Wang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-12 with Mathematics categories.

The parabolic partial differential equations model one of the most important processes in the real-world: diffusion. Whether it is the diffusion of energy in space-time, the diffusion of species in ecology, the diffusion of chemicals in biochemical processes, or the diffusion of information in social networks, diffusion processes are ubiquitous and crucial in the physical and natural world as well as our everyday lives. This book is self-contained and covers key topics such as the Lp theory and Schauder theory, maximum principle, comparison principle, regularity and uniform estimates, initial-boundary value problems of semilinear parabolic scalar equations and weakly coupled parabolic systems, the upper and lower solutions method, monotone properties and long-time behaviours of solutions, convergence of solutions and stability of equilibrium solutions, global solutions and finite time blowup. It also touches on periodic boundary value problems, free boundary problems, and semigroup theory. The book covers major theories and methods of the field, including topics that are useful but hard to find elsewhere. This book is based on tried and tested teaching materials used at the Harbin Institute of Technology over the past ten years. Special care was taken to make the book suitable for classroom teaching as well as for self-study among graduate students. About the Author: Mingxin Wang is Professor of Mathematics at Harbin Institute of Technology, China. He has published ten monographs and textbooks and 260 papers. He is also a supervisor of 30 PhD students.

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.

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.

Handbook Of Nonlinear Partial Differential Equations

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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2004-06-02

Handbook Of Nonlinear Partial Differential Equations written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-02 with Mathematics categories.

The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:

Partial Differential Equations Of Parabolic Type

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Author : Avner Friedman
language : en
Publisher: Courier Corporation
Release Date : 2013-08-16

Partial Differential Equations Of Parabolic Type written by Avner Friedman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-16 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.

Second Order Partial Differential Equations In Hilbert Spaces

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Author : Giuseppe Da Prato
language : en
Publisher: Cambridge University Press
Release Date : 2002-07-25

Second Order Partial Differential Equations In Hilbert Spaces written by Giuseppe Da Prato and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-25 with Mathematics categories.

Second order linear parabolic and elliptic equations arise frequently in mathematics and other disciplines. For example parabolic equations are to be found in statistical mechanics and solid state theory, their infinite dimensional counterparts are important in fluid mechanics, mathematical finance and population biology, whereas nonlinear parabolic equations arise in control theory. Here the authors present a state of the art treatment of the subject from a new perspective. The main tools used are probability measures in Hilbert and Banach spaces and stochastic evolution equations. There is then a discussion of how the results in the book can be applied to control theory. This area is developing very rapidly and there are numerous notes and references that point the reader to more specialised results not covered in the book. Coverage of some essential background material will help make the book self-contained and increase its appeal to those entering the subject.