压差方程的一维活塞问题

上海大学学报(自然科学版) ›› 2009, Vol. 15 ›› Issue (4): 388-393.

压差方程的一维活塞问题

张利英盛万成

上海大学理学院,上海 200444

收稿日期:2008-04-03 出版日期:2009-08-30 发布日期:2009-08-30

One-Dimensional Piston Problem of Pressure-Gradient Equations

College of Sciences, Shanghai University, Shanghai 200444, China

Received:2008-04-03 Online:2009-08-30 Published:2009-08-30
Contact: 盛万成(1963～)，男，教授，博士生导师，研究方向为非线性偏微分方程. E-mail:mathwcsheng@shu.edu.cn

摘要/Abstract

摘要：

用改进的Glimm格式的方法, 研究压差方程的一维活塞问题：当活塞的运动速度是一个常数的扰动时,含有激波的弱解的存在性.对波的相互作用以及扰动波在主激波和活塞上的反射给出了精确的估计,在对主激波的强度不加限制的情况下证明激波解的整体存在性.

关键词: 活塞问题；压差方程；激波；Glimm格式

Abstract:

This paper uses the improved Glimm scheme to study a one-dimensional problem for the pressure gradient equations when the speed of piston is a constant disturbance. We show existence of the weak solution containing shock waves. Using the modified Glimm scheme, we give global existence of shock front solution to this problem in bounded varition (BV) space. 

Key words: piston problem; pressure gradient equations; shock wave solution; Glimm scheme

中图分类号:

O175.27

张利英盛万成. 压差方程的一维活塞问题[J]. 上海大学学报(自然科学版), 2009, 15(4): 388-393.

ZHANG Li-Yang, CHENG Mo-Cheng. One-Dimensional Piston Problem of Pressure-Gradient Equations[J]. Journal of Shanghai University（Natural Science Edition）, 2009, 15(4): 388-393.