# Diffusion Equations

Share this page
*Seizô Itô*

This book presents a self-contained exposition of the theory of initial-boundary value problems for diffusion equations. Intended as a graduate textbook, the book is of interest to mathematicians as well as theoretical physicists. Because it uses as little knowledge of functional analysis as possible, the book is accessible to those with a background in multivariable calculus, elementary Lebesgue integral theory, and basic parts of the theory of integral equations. Itô treats diffusion equations with variable coefficients associated with boundary conditions and the corresponding elliptic differential equations. The fundamental solution of the initial-boundary value problem and Green's function for the elliptic boundary value problem are constructed, and the existence of solutions of these problems is proved. In addition, the book discusses several important properties of the solutions.

#### Table of Contents

# Table of Contents

## Diffusion Equations

- Cover Cover11
- Title page iii4
- Contents v6
- Preface to the English Edition vii8
- Preface to the Japanese Edition ix10
- Introduction 112
- Chapter 1. Fundamental solutions of diffusion equations in Euclidean spaces 2536
- Chapter 2. Diffusion equations in a bounded domain 4152
- Chapter 3. Diffusion equations in unbounded domains 91102
- Chapter 4. Elliptic boundary value problems 147158
- Chapter 5. Some related topics in vector analysis 209220
- Supplementary Notes and References 221232
- Subject Index 225236
- Back Cover Back Cover1241