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The Porous Medium Equation


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Table of Contents

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


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 in this work. mathematical reviews This book is a pleasure to read. It will be an excellent source, allowing the reader to build a proper intuition and to understand the basic facts of the theory.

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