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.

Readership

Graduate students of pure and applied mathematics and of theoretical physics.

Table of Contents

• Fundamental solutions of diffusion equations in Euclidean spaces
• Diffusion equations in a bounded domain
• Diffusion equations in unbounded domains
• Elliptic boundary value problems
• Some related topics in vector analysis