Nonlinear nonlocal equations in the theory of waves
著者
書誌事項
Nonlinear nonlocal equations in the theory of waves
（Translations of mathematical monographs, v. 133）
American Mathematical Society, c1994
- タイトル別名
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Нелинейные нелокальные уравнения в теории волн
Nelineĭnye nelokalʹnye uravnenii︠a︡ v teorii voln
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注記
Includes bibliographical references
内容説明・目次
内容説明
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 blow-up 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 priori 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.
目次
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 Kolmogorov-Petrovskii-Piskunov equation Asymptotics of solutions of the Whitham equation for large times Asymptotics as $t\rightarrow \infty$ of solutions of the nonlinear nonlocal Schrodinger equation Asymptotics of solutions for a system of equations of surface waves for large times The step-decaying problem for the Korteweg-de Vries-Burgers equation References.
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