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The Porous Medium Equation
Mathematical Theory
Juan Luis Vazquez
648 pages
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234x156mm
978-0-19-856903-9
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Hardback
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26 October 2006
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- Systematic and comprehensive presentation
- Detailed introductions to chapters
- End of chapter notes provide comments, historical notes and recommended reading
- Provides end of chapter exercises to consolidate the text
- Extensive bibliography
The Heat Equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it come to be fairly well understood. In this monograph, aimed at research students and academics in mathematics and engineering, as well as engineering specialists, Professor Vazquez provides a systematic and comprehensive presentation of the mathematical theory of the nonlinear heat equation usually called the Porous Medium Equation (PME). This equation appears in a number of physical applications, such as to describe processes involving fluid flow, heat transfer or diffusion. Other applications
have been proposed in mathematical biology, lubrication, boundary layer theory, and other fields. Each chapter contains a detailed introduction and is supplied with a section of notes, providing comments, historical notes or recommended reading, and exercises for the reader.Readership: Research students and academics in mathematics and engineering, as well as engineering specialists.
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Juan Luis Vazquez, Universidad Autónoma de Madrid
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"The author of this monograph skillfully guides the reader, whether mathematician or physicist, through the background needed to understand and use the modern techniques developed...This book is a pleasure to read. It will be an excellent source, allowing the reader to build a proper intuition and of understand the basic facts of the theory...This book is also strongly recommended to researchers in Applied Mathematics who study various linear and nonlinear phenomena, but it may also be useful and comprehensive for a broader community od mathmaticians, physicists and engineers. I deeply believe that the present book is one of the most important works in its fieldthat have appeared until now...beautifully writtien and well organized, and I strongly
recommend this book to anyone seeking a stylish, balanced, up-to-date survey of this central area of nonlinear partial differential equations." - Vicentiu Rãdulescu Mathmatical Reviews
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Preface
1: Introduction
Part 1
2: Main applications
3: Preliminaries and basic estimates
4: Basic examples
5: The Dirichlet problem I. Weak solutions
6: The Dirichlet problem II. Limit solutions, very weak solutions and some other variants
7: Continuity of local solutions
8: The Dirichlet problem III. Strong solutions
9: The Cauchy problem. L' theory
10: The PME as an abstract evolution equation. Semigroup approach
11: The Neumann problem and problems on manifolds
Part 2
12: The Cauchy problem with growing initial data
13: Optimal existence theory for nonnegative solutions
14: Propagation properties
15: One-dimensional theory. Regularity and interfaces
16: Full analysis of selfsimilarity
17: Techniques of symmetrization and concentration
18: Asymptotic behaviour I. The Cauchy problem
19: Regularity and finer asymptotics in several dimensions
20: Asymptotic behaviour II. Dirichlet and Neumann problems
Complements
21: Further applications
22: Basic facts and appendices
Bibliography
Index
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The specification in this catalogue, including without limitation price, format, extent, number of illustrations, and month of publication, was as accurate as possible at the time the catalogue was compiled. Occasionally, due to the nature of some contractual restrictions, we are unable to ship a specific product to a particular territory. Jacket images are provisional and liable to change before publication.
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