Translations of Mathematical Monographs 1994; 289 pp; hardcover Volume: 133 ISBN10: 082184573X ISBN13: 9780821845738 List Price: US$117 Member Price: US$93.60 Order Code: MMONO/133
 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. Readership Specialists in partial differential equations. 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 Table of Contents  Introduction
 Simplest properties of solutions of nonlinear nonlocal equations
 The Cauchy problem for the Whitham equation
 The periodic problem
 The system of equations of surface waves
 Generalized solutions
 The asymptotics as \(t\rightarrow \infty\) of solutions of the generalized KolmogorovPetrovskiĭPiskunov equation
 Asymptotics of solutions of the Whitham equation for large times
 Asymptotics as \(t\rightarrow \infty\) of solutions of the nonlinear nonlocal Schrödinger equation
 Asymptotics of solutions for a system of equations of surface waves for large times
 The stepdecaying problem for the Kortewegde VriesBurgers equation
 References
