Global Solutions And The Asymptotic Behavior For Nonlinear Wave Equations With Small Initial Data 9784864970549

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Название: Global Solutions And The Asymptotic Behavior For Nonlinear Wave Equations With Small Initial Data
ISBN: 9784864970549
Издательство: World Scientific Publishing
Классификация:

Основы высшей математики и математический анализ

Дифференциальное исчисление и дифференциальные уравнения

ISBN-10: 4864970548
Обложка/Формат: Paperback
Страницы: 298
Вес: 0.00 кг.
Дата издания: 01.11.2017
Серия: Mathematics
Язык: English
Читательская аудитория: College/higher education
Ключевые слова: Differential calculus & equations, MATHEMATICS / Differential Equations / Partial,SCIENCE / Mechanics / Fluids,TECHNOLOGY & ENGINEERING / Acoustics & Sound
Поставляется из: Англии
Описание: In the study of the Cauchy problem for nonlinear wave equations with small initial data, the case where the nonlinearity has the critical power is of special interest. In this case, depending on the structure of the nonlinearity, one may observe global existence and finite time blow-up of solutions. In 80s, Klainerman introduced a sufficient condition, called the null condition, for the small data global existence in the critical case. Recently, weaker sufficient conditions are also studied.This volume offers a comprehensive survey of the theory of nonlinear wave equations, including the classical local existence theorem, the global existence in the supercritical case, the finite time blow-up and the lifespan estimate in the critical case, and the global existence under the null condition in two and three space dimensions. The main tool here is the so-called vector field method. This volume also contains recent progress in the small data global existence under some conditions weaker than the null condition, and it is shown that a wide variety of the asymptotic behavior is observed under such weaker conditions.This volume is written not only for researchers, but also for graduate students who are interested in nonlinear wave equations. The exposition is intended to be self-contained and a complete proof is given for each theorem.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets

Global Solutions And The Asymptotic Behavior For Nonlinear Wave Equations With Small Initial Data,