Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2009; 46(3): 409-434

Printed May 1, 2009

https://doi.org/10.4134/BKMS.2009.46.3.409

Copyright © The Korean Mathematical Society.

The generalized Riemann problem for first order quasilinear hyperbolic systems of conservation laws I

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

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