ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR GENERALIZED BURGERS EQUATION

作     者：徐艳玲 蒋咪娜 Xu Yanling Department of Mathematics and Information Science, Basic Sciences, Huazhong Agricultural University, Wuhan 430070, ChinaJiang Mina Department of Mathematical and Statistical Sciences, Central China Normal University,Wuhan 430079, China

作者机构：Department of Mathematics and Information Science Basic Sciences Huazhong Agricultural University Wuhan 430070 China Department of Mathematical and Statistical Sciences Central China Normal UniversityWuhan 430079 China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2005年第25卷第1期

页      面：119-129页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：TheresearchwassupportedbythreegrantsfromtheNationalNaturalScienceFoundationofChina(10171037)thescientificresearchsystemsofHuazhongAgriculturalUniversityYoungerScienceFoundation(10401021) 

主　　题：Burgers equation rarefaction wave the method of successive approximation maximum principle a priori estimatc stability 

摘      要：This paper is concerned with the stability of the rarefaction wave for the Burgers equationwhere 0 ≤ a 1/4p (q is determined by (2.2)). Roughly speaking, under the assumption that u_ u+, the authors prove the existence of the global smooth solution to the Cauchy problem (I), also find the solution u(x, t) to the Cauchy problem (I) satisfying sup |u(x, t) -uR(x/t)| → 0 as t → ∞, where uR(x/t) is the rarefaction wave of the non-viscous Burgersequation ut + f(u)x = 0 with Riemann initial data u(x, 0) =