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

Title & Authors
THE GENERALIZED RIEMANN PROBLEM FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS I
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 = $\small{U{(\frac{x}{t})}}$ 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
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