DOI QR코드

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

  • Chen, Shouxin ;
  • Huang, Decheng ;
  • Han, Xiaosen
  • Published : 2009.05.31

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 = $U{(\frac{x}{t})}$ 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

References

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