eBook ISBN:  9781470445256 
Product Code:  MMONO/114.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
eBook ISBN:  9781470445256 
Product Code:  MMONO/114.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 

Book DetailsTranslations of Mathematical MonographsVolume: 114; 1992; 225 ppMSC: Primary 35
This book presents a selfcontained exposition of the theory of initialboundary 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 initialboundary 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.
ReadershipGraduate students of pure and applied mathematics and of theoretical physics.

Table of Contents

Chapters

Introduction

Chapter 1. Fundamental solutions of diffusion equations in Euclidean spaces

Chapter 2. Diffusion equations in a bounded domain

Chapter 3. Diffusion equations in unbounded domains

Chapter 4. Elliptic boundary value problems

Chapter 5. Some related topics in vector analysis


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This book presents a selfcontained exposition of the theory of initialboundary 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 initialboundary 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.
Graduate students of pure and applied mathematics and of theoretical physics.

Chapters

Introduction

Chapter 1. Fundamental solutions of diffusion equations in Euclidean spaces

Chapter 2. Diffusion equations in a bounded domain

Chapter 3. Diffusion equations in unbounded domains

Chapter 4. Elliptic boundary value problems

Chapter 5. Some related topics in vector analysis