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   作者單位： 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： 數學物理學報（英文版）  ISTIC SCI 英文刊名： ACTA MATHEMATICA SCIENTIA  年，卷(期)： 2005 25(1)  分類號：   關鍵詞： Burgers equation   rarefaction wave   the method of successive approximation   maximum principle   a priori estimate   stability  

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