ON INTERACTION OF SHOCK AND SOUND WAVE (Ⅰ)

作     者：CHEN SHUXING(Institute of Mathematics, Fudan University Shanghai 200433, China.) 

作者机构：复旦大学数学系 上海 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：1996年第17卷第4期

页      面：35-42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：国家教育部项目 国家自然科学基金 

主　　题：Shock wave Sound wave Nonliner hyperbolic system Asymptotic solution 

摘      要：This paper studies the ioteraction of shock and gradient wave (sound wave) of solutions to the system of inviscid isentropic gas dynamics as a model for the corresponding problems for nonlinear hyperbolic systems. The problem can be reduced to a boundary value problem in a wedged domain. By using the method of constructing asymptotic solutions and Newton’s iteration process it is proved that if a weak shock hits a gradient wave, then the grandient wave will split into two gradient waves, while the shock continuses propagating. In this paper the author reduces the problem to a standard form and constructs asymptotic solution of the problem. The existence of the genuine solution will be given in the following paper.