Second Order Parabolic Differential Equations

Gary M Lieberman

• Publisher: World Scientific
• Year: 1996
• Print ISBN: 9789810228835, 9789810228835
• eBook ISBN: 9789812819796
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

This book is an introduction to the general theory of second order parabolic differential equations, which model many important, time-dependent physical systems. It studies the existence, uniqueness, and regularity of solutions to a variety of problems with Dirichlet boundary conditions and general linear and nonlinear boundary conditions by means of a priori estimates. The first seven chapters give a description of the linear theory and are suitable for a graduate course on partial differential equations. The last eight chapters cover the nonlinear theory for smooth solutions. They include much of the author's research and are aimed at researchers in the field. A unique feature is the emphasis on time-varying domains.

Table of contents

• CONTENTS
• PREFACE
• PREFACE TO REVISED EDITION
• CHAPTER I INTRODUCTION
• CHAPTER II MAXIMUM PRINCIPLES
• CHAPTER III INTRODUCTION TO THE THEORY OF WEAK SOLUTIONS
• CHAPTER IV HÖLDER ESTIMATES
• CHAPTER V EXISTENCE, UNIQUENESS AND REGULARITYOF SOLUTIONS
• CHAPTER VI FURTHER THEORY OF WEAK SOLUTIONS
• CHAPTER VII STRONG SOLUTIONS
• CHAPTER VIII FIXED POINT THEOREMS AND THEIR APPLICATIONS
• CHAPTER IX COMPARISON AND MAXIMUM PRINCIPLES
• CHAPTER X BOUNDARY GRADIENT ESTIMATES
• CHAPTER XI GLOBAL AND LOCAL GRADIENT BOUNDS
• CHAPTER X HÖLDER GRADIENT ESTIMATES AND EXISTENCE THEOREMS
• CHAPTER XIII THE OBLIQUE DERIVATIVE PROBLEM FOR QUASILINEAR PARABOLIC EQUATIONS
• CHAPTER XIV FULLY NONLINEAR EQUATIONS I.INTRODUCTION
• CHAPTER XV FULLY NONLINEAR EQUATIONS II. HESSIAN EQUATIONS
• Bibliography
• Index