THE GENERALIZED RIEMANN PROBLEM FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS I

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 46, Issue 3, 2009, pp.409-434
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2009.46.3.409

Title & Authors

THE GENERALIZED RIEMANN PROBLEM FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS I

Chen, Shouxin; Huang, Decheng; Han, Xiaosen;

Chen, Shouxin; Huang, Decheng; Han, Xiaosen;

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 = of the correspondin 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;

Language

English

Cited by

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