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

Reviews

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.