数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (4): 777-802.doi: 10.1016/S0252-9602(09)60070-9

• 论文 •    下一篇

TWO-DIMENSIONAL RIEMANN PROBLEMS: FROM SCALAR CONSERVATION LAWS TO COMPRESSIBLE EULER EQUATIONS

李杰权,盛万成,张同,郑玉玺   

  1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;Department of Mathematics, Shanghai University, Shanghai 200444, China;Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, China;Department of Mathematics, The Pennsylvania State University, UP, PA 16802, USA
  • 收稿日期:2008-12-29 出版日期:2009-07-20 发布日期:2009-07-20
  • 基金资助:

    The research of Li partially supported by 973 Key program and the Key Program from Beijing Educational Commission with No. KZ200910028002, Program for New Century Excellent Talents in University (NCET) and Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR-IHLB); The research of Sheng partially supported by NSFC (10671120) and Shanghai Leading Academic Discipline Project: J50101; The research of Zhang partially supported by NSFC (10671120); The research of Zheng partially supported by NSF-DMS-0603859

TWO-DIMENSIONAL RIEMANN PROBLEMS: FROM SCALAR CONSERVATION LAWS TO COMPRESSIBLE EULER EQUATIONS

 LI Jie-Quan, CHENG Mo-Cheng, ZHANG Tong, ZHENG Yu-Xi   

  1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;Department of Mathematics, Shanghai University, Shanghai 200444, China;Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, China;Department of Mathematics, The Pennsylvania State University, UP, PA 16802, USA
  • Received:2008-12-29 Online:2009-07-20 Published:2009-07-20
  • Supported by:

    The research of Li partially supported by 973 Key program and the Key Program from Beijing Educational Commission with No. KZ200910028002, Program for New Century Excellent Talents in University (NCET) and Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR-IHLB); The research of Sheng partially supported by NSFC (10671120) and Shanghai Leading Academic Discipline Project: J50101; The research of Zhang partially supported by NSFC (10671120); The research of Zheng partially supported by NSF-DMS-0603859

摘要:

In this paper we survey the authors’ and related work on two-dimensional Rie-mann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections: 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.

关键词: two-dimensional Riemann problem, compressible Euler equation, reflection of shocks, interaction of rarefaction waves, delta-shocks

Abstract:

In this paper we survey the authors’ and related work on two-dimensional Rie-mann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections: 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.

Key words: two-dimensional Riemann problem, compressible Euler equation, reflection of shocks, interaction of rarefaction waves, delta-shocks

中图分类号: 

  • 35L65