数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (1): 261-271.doi: 10.1007/s10473-020-0118-8

• 论文 • 上一篇    下一篇

GLOBAL SIMPLE WAVE SOLUTIONS TO A KIND OF TWO DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS

刘见礼, 薛杰   

  1. Department of Mathematics, Shanghai University, Shanghai 200444, China
  • 收稿日期:2018-09-11 修回日期:2019-01-06 出版日期:2020-02-25 发布日期:2020-04-14
  • 通讯作者: Jie XUE E-mail:jiexue@163.com
  • 基金资助:
    This work was supported by NSFC (11771274, 11401367).

GLOBAL SIMPLE WAVE SOLUTIONS TO A KIND OF TWO DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS

Jianli LIU, Jie XUE   

  1. Department of Mathematics, Shanghai University, Shanghai 200444, China
  • Received:2018-09-11 Revised:2019-01-06 Online:2020-02-25 Published:2020-04-14
  • Contact: Jie XUE E-mail:jiexue@163.com
  • Supported by:
    This work was supported by NSFC (11771274, 11401367).

摘要: This paper is concerned with the simple waves of a kind of two dimensional hyperbolic system of conservation laws, which can be obtained from the two dimensional relativistic membrane equation in Minkowski space. Using wave decomposition method, we get that a flow adjacent to a nonconstant state can be a global simple wave. Furthermore, the flow is covered by three families of characteristics, in which the first family of characteristics is straight and the others are curved, which is different to the almost related results.

关键词: global simple wave solutions, conservation laws, relativistic membrane equation

Abstract: This paper is concerned with the simple waves of a kind of two dimensional hyperbolic system of conservation laws, which can be obtained from the two dimensional relativistic membrane equation in Minkowski space. Using wave decomposition method, we get that a flow adjacent to a nonconstant state can be a global simple wave. Furthermore, the flow is covered by three families of characteristics, in which the first family of characteristics is straight and the others are curved, which is different to the almost related results.

Key words: global simple wave solutions, conservation laws, relativistic membrane equation

中图分类号: 

  • 35L51