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Softcover ISBN:  9780821846858 
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Softcover ISBN:  9780821846858 
Product Code:  MMONO/95.S 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445072 
Product Code:  MMONO/95.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Softcover ISBN:  9780821846858 
eBook ISBN:  9781470445072 
Product Code:  MMONO/95.S.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 95; 1991; 251 ppMSC: Primary 35
This book addresses a class of equations central to many areas of mathematics and its applications. Although there is no routine way of solving nonlinear partial differential equations, effective approaches that apply to a wide variety of problems are available. This book addresses a general approach that consists of the following: Choose an appropriate function space, define a family of mappings, prove this family has a fixed point, and study various properties of the solution. The author emphasizes the derivation of various estimates, including a priori estimates. By focusing on a particular approach that has proven useful in solving a broad range of equations, this book makes a useful contribution to the literature.

Table of Contents

Chapters

Introduction

Notes for the English Translation

Chapter I. The first boundary value problem for secondorder quasilinear parabolic equations with principal part in divergence form

Chapter II. A periodic boundary value problem for a nonlinear telegraph equation

Chapter III. The initial value problem for a nonlinear Schrödinger equation

Chapter IV. Multidimensional subsonic flows around an obstacle

Chapter V. The initialboundary value problem for degenerate quasilinear parabolic equations

Chapter VI. The speed of propagation of the solution of a degenerate quasilinear parabolic equation

Chapter VII. Aleksandrov and Bony maximum principles for parabolic equations

Chapter VIII. The density theorem and its applications

Chapter IX. Fully nonlinear parabolic equations

Chapter X. Fully nonlinear parabolic equations (continued)


Reviews

Serves as a good introduction for postgraduate students ... For advanced researchers, it is also a good reference to many useful results and to various kinds of techniques.
Bulletin of the London Mathematical Society 
A wellwritten and instructive collection of recent results on various topics in the field of nonlinear secondorder PDEs ... the exposition is exceptionally clear; Tso has provided a competent and very readable translation.
Mathematical Reviews 
Clearly written, its global quality is good.
Zentralblatt MATH


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This book addresses a class of equations central to many areas of mathematics and its applications. Although there is no routine way of solving nonlinear partial differential equations, effective approaches that apply to a wide variety of problems are available. This book addresses a general approach that consists of the following: Choose an appropriate function space, define a family of mappings, prove this family has a fixed point, and study various properties of the solution. The author emphasizes the derivation of various estimates, including a priori estimates. By focusing on a particular approach that has proven useful in solving a broad range of equations, this book makes a useful contribution to the literature.

Chapters

Introduction

Notes for the English Translation

Chapter I. The first boundary value problem for secondorder quasilinear parabolic equations with principal part in divergence form

Chapter II. A periodic boundary value problem for a nonlinear telegraph equation

Chapter III. The initial value problem for a nonlinear Schrödinger equation

Chapter IV. Multidimensional subsonic flows around an obstacle

Chapter V. The initialboundary value problem for degenerate quasilinear parabolic equations

Chapter VI. The speed of propagation of the solution of a degenerate quasilinear parabolic equation

Chapter VII. Aleksandrov and Bony maximum principles for parabolic equations

Chapter VIII. The density theorem and its applications

Chapter IX. Fully nonlinear parabolic equations

Chapter X. Fully nonlinear parabolic equations (continued)

Serves as a good introduction for postgraduate students ... For advanced researchers, it is also a good reference to many useful results and to various kinds of techniques.
Bulletin of the London Mathematical Society 
A wellwritten and instructive collection of recent results on various topics in the field of nonlinear secondorder PDEs ... the exposition is exceptionally clear; Tso has provided a competent and very readable translation.
Mathematical Reviews 
Clearly written, its global quality is good.
Zentralblatt MATH