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

• Published in: Acta mathematica scientia Vol. 29; no. 4; pp. 777 - 802
• Main Author: 李杰权 盛万成 张同 郑玉玺
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2009; 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
• Subjects: 35L65; 35L67; 76J20; 76N15; compressible Euler equation; delta-shocks; interaction of rarefaction waves; reflection of shocks; Riemann问题; two-dimensional Riemann problem; 双曲型守恒律; 可压缩Euler方程; 气体动力学; reflection of shocks; 76N15; delta-shocks; compressible Euler equation; 76J20; 35L67; two-dimensional Riemann problem; 35L65; interaction of rarefaction waves
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(09)60070-9

In this paper we survey the authors＇ and related work on two-dimensional Riemann 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.