- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 The generalized Riemann problem for first order quasilinear hyperbolic systems of conservation laws I Bull. Korean Math. Soc. 2009 Vol. 46, No. 3, 409-434 https://doi.org/10.4134/BKMS.2009.46.3.409Printed May 1, 2009 Shouxin Chen, Decheng Huang, and Xiaosen Han Henan University, Xinyang Vocational Technical College, and Henan University Abstract : In this paper, we consider a generalized Riemann problem of the first order hyperbolic conservation laws. For the case that excludes the centered wave, we prove that the generalized Riemann problem admits a unique piecewise smooth solution $u=u(t,x)$, and this solution has a structure similar to the similarity solution $u=U\left(\frac{x}{t}\right)$ of the corresponding Riemann problem in the neighborhood of the origin provided that the coefficients of the system and the initial conditions are sufficiently smooth. Keywords : quasilinear hyperbolic systems, generalized Riemann problem, local solution MSC numbers : 35L45, 35A07 Downloads: Full-text PDF