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ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR GENERALIZED BURGERS EQUATION
This paper is concerned with the stability of the rarefaction wave for the Burgers equation{ ut+f(u)x=μtαuxx, μ＞0, x∈R, t＞0, (Ⅰ)u|t=o = u0(x) →u± , x →∞ ,where 0 ≤α＜ 1/4q (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)-x∈RuR(x/t)| → 0 as t →∞, where uR(x/t) is the rarefaction wave of the non-viscous Burgers equation ut + f(u)x = 0 with Riemann initial data u(x, 0) ={u_,x＜0, u+, x＞0.
作 者： Xu Yanling Jiang Mina 作者单位： Xu Yanling(Department of Mathematics and Information Science, Basic Sciences, Huazhong Agricultural University, Wuhan 430070, China)Jiang Mina(Department of Mathematical and Statistical Sciences, Central China Normal University, Wuhan 430079, China)
刊 名： 数学物理学报（英文版） ISTIC SCI 英文刊名： ACTA MATHEMATICA SCIENTIA 年，卷(期)： 2005 25(1) 分类号： 关键词： Burgers equation rarefaction wave the method of successive approximation maximum principle a priori estimate stability【ASYMPTOTIC STABILITY OF RAREFACTION 】相关文章：
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