用L^2能量法研究粘性守恒律解的渐近性态(英文)  

Asymptotic Behaviors of Solutions to Viscous Conservation Laws via L^2-energy Method

作　　者：Kenji Nishihara 

机构地区：[1]早稻田大学

出　　处：《数学进展》2001年第4期293-321,共29页Advances in Mathematics（China）

摘　　要：本文讨论单个粘性守恒律方程与具有粘性的ｐ方程组的Ｃａｕｃｈｙ问题．根据初始资料的不同情形，其相应的Ｒｉｅｍａｎｎ问题以疏散波，激波或它们的迭加为弱解．本文的目的是指出Ｃａｕｃｈｙ问题的解将分别趋于疏散波，激波或它们的迭加．本文基本方法是能量积分法．文中综述了现有的成果，也提出了一些未解决的问题．We consider the Cauchy problems for both scalar viscous conservation law and psystem with viscosity, the corresponding riemann problems have the nonlinear waves as the weak solutions, i. e. the rarefaction wave, the shock wave or their superpositions, depending on the data. Our purpose is to show that the solutions to the cauchy problems end to the rarefaction wave, viscous shock wave or their superposions, respectively. Fundamental results are proved via the L2-energy method, and the recent results are surveyed. Some cases are proposed as open problems.

关 键 词：粘性守恒律 p方程组 疏散波 粘性激波 能量积分法 RIEMANN问题 CAUCHY问题 粘性Burgers方程 

分 类 号：O175.1[理学—数学]