书目名称 | Nonlinear Partial Differential Equations |
副标题 | Asymptotic Behavior |
编辑 | Mi-Ho Giga,Yoshikazu Giga,Jürgen Saal |
视频video | http://file.papertrans.cn/668/667626/667626.mp4 |
概述 | Challenges the reader with many exercises, examples and illustrations.Includes recent developments and several open problems.Serves as an excellent textbook for a first course in modern analysis or as |
丛书名称 | Progress in Nonlinear Differential Equations and Their Applications |
图书封面 |  |
描述 | The purpose of this book is to present typical methods (including rescaling methods) for the examination of the behavior of solutions of nonlinear partial di?erential equations of di?usion type. For instance, we examine such eq- tions by analyzing special so-called self-similar solutions. We are in particular interested in equations describing various phenomena such as the Navier– Stokesequations.Therescalingmethod describedherecanalsobeinterpreted as a renormalization group method, which represents a strong tool in the asymptotic analysis of solutions of nonlinear partial di?erential equations. Although such asymptotic analysis is used formally in various disciplines, not seldom there is a lack of a rigorous mathematical treatment. The intention of this monograph is to ?ll this gap. We intend to develop a rigorous mat- matical foundation of such a formalasymptotic analysis related to self-similar solutions. A self-similar solution is, roughly speaking, a solution invariant under a scaling transformationthat does not change the equation. For several typical equations we shall give mathematical proofs that certain self-similar solutions asymptotically approximate the typical behavio |
出版日期 | Textbook 2010 |
关键词 | Burgers vortex; Navier-Stokes equations; asymptotic behavior; calculus; calculus inequalities; compactnes |
版次 | 1 |
doi | https://doi.org/10.1007/978-0-8176-4651-6 |
isbn_ebook | 978-0-8176-4651-6Series ISSN 1421-1750 Series E-ISSN 2374-0280 |
issn_series | 1421-1750 |
copyright | Springer Science+Business Media, LLC 2010 |