Hardcover ISBN:  9780821845738 
Product Code:  MMONO/133 
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eBook ISBN:  9781470445416 
Product Code:  MMONO/133.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821845738 
eBook: ISBN:  9781470445416 
Product Code:  MMONO/133.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 
Hardcover ISBN:  9780821845738 
Product Code:  MMONO/133 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445416 
Product Code:  MMONO/133.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821845738 
eBook ISBN:  9781470445416 
Product Code:  MMONO/133.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: 133; 1994; 289 ppMSC: Primary 35; 45; Secondary 76
This book is the first to concentrate on the theory of nonlinear nonlocal equations. The authors solve a number of problems concerning the asymptotic behavior of solutions of nonlinear evolution equations, the blowup of solutions, and the global in time existence of solutions. In addition, a new classification of nonlinear nonlocal equations is introduced. A large class of these equations is treated by a single method, the main features of which are apriori estimates in different integral norms and use of the Fourier transform. This book will interest specialists in partial differential equations, as well as physicists and engineers.
ReadershipSpecialists in partial differential equations.

Table of Contents

Chapters

Introduction

Chapter 1. Simplest properties of solutions of nonlinear nonlocal equations

Chapter 2. The Cauchy problem for the Whitham equation

Chapter 3. The periodic problem

Chapter 4. The system of equations of surface waves

Chapter 5. Generalized solutions

Chapter 6. The asymptotics as $t > (\infty )$ of solutions of the generalized KolmogorovPetrovskiiPiskunov equation

Chapter 7. Asymptotics of solutions of the Whitham equation for large times

Chapter 8. Asymptotics as $t > (\infty )$ of solutions of the nonlinear nonlocal Schrodinger equation

Chapter 9. Asymptotics of solutions for a system of equations of surface waves for large times

Chapter 10. The stepdecaying problem for the Kortewegde VriesBurgers equation


Reviews

The book is a good exposition of important results. Many examples are considered. The style of the book is systematic and readable.
Zentralblatt MATH 
ExcellenDt contribution to the study of wave propagation...
Mathematical Reviews 
Very readable ... will be a source of inspiration not only to those who study nonlinear wave equations, but to all who like to see hard problems solved by masterful use of basic techniques.
Bulletin of the AMS


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This book is the first to concentrate on the theory of nonlinear nonlocal equations. The authors solve a number of problems concerning the asymptotic behavior of solutions of nonlinear evolution equations, the blowup of solutions, and the global in time existence of solutions. In addition, a new classification of nonlinear nonlocal equations is introduced. A large class of these equations is treated by a single method, the main features of which are apriori estimates in different integral norms and use of the Fourier transform. This book will interest specialists in partial differential equations, as well as physicists and engineers.
Specialists in partial differential equations.

Chapters

Introduction

Chapter 1. Simplest properties of solutions of nonlinear nonlocal equations

Chapter 2. The Cauchy problem for the Whitham equation

Chapter 3. The periodic problem

Chapter 4. The system of equations of surface waves

Chapter 5. Generalized solutions

Chapter 6. The asymptotics as $t > (\infty )$ of solutions of the generalized KolmogorovPetrovskiiPiskunov equation

Chapter 7. Asymptotics of solutions of the Whitham equation for large times

Chapter 8. Asymptotics as $t > (\infty )$ of solutions of the nonlinear nonlocal Schrodinger equation

Chapter 9. Asymptotics of solutions for a system of equations of surface waves for large times

Chapter 10. The stepdecaying problem for the Kortewegde VriesBurgers equation

The book is a good exposition of important results. Many examples are considered. The style of the book is systematic and readable.
Zentralblatt MATH 
ExcellenDt contribution to the study of wave propagation...
Mathematical Reviews 
Very readable ... will be a source of inspiration not only to those who study nonlinear wave equations, but to all who like to see hard problems solved by masterful use of basic techniques.
Bulletin of the AMS