The Porous Medium Equation

Mathematical Theory

Juan Luis Vazquez - Collection Oxford Mathematical Monographs

624 pages, parution le 26/10/2006

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Résumé

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.

L'auteur - Juan Luis Vazquez

Juan Luis Vazquez, Universidad Autónoma de Madrid

Sommaire

Preface
Introduction
Part 1
- Main applications
- Preliminaries and basic estimates
- Basic examples
- The Dirichlet problem I. Weak solutions
- The Dirichlet problem II. Limit solutions, very weak solutions and some other variants
- Continuity of local solutions
- The Dirichlet problem III. Strong solutions
- The Cauchy problem. L' theory
- The PME as an abstract evolution equation. Semigroup approach
- The Neumann problem and problems on manifolds
Part 2
- The Cauchy problem with growing initial data
- Optimal existence theory for nonnegative solutions
- Propagation properties
- One-dimensional theory. Regularity and interfaces
- Full analysis of selfsimilarity
- Techniques of symmetrization and concentration
- Asymptotic behaviour I. The Cauchy problem
- Regularity and finer asymptotics in several dimensions
- Asymptotic behaviour II. Dirichlet and Neumann problems
Complements
- Further applications
- Basic facts and appendices
Bibliography
Index

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	PAPIER
Éditeur(s)	Oxford University Press
Auteur(s)	Juan Luis Vazquez
Collection	Oxford Mathematical Monographs
Parution	26/10/2006
Nb. de pages	624
Format	16 x 24
Couverture	Relié
Poids	1065g
Intérieur	Noir et Blanc
EAN13	9780198569039
ISBN13	978-0-19-856903-9