Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE GENERALIZED RIEMANN PROBLEM FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS I

  • Chen, Shouxin (COLLEGE OF MATHEMATICS AND INFORMATION SCIENCE) ;
  • Huang, Decheng (DEPARTMENT OF MATHEMATICS XINYANG VOCATIONAL TECHNICAL COLLEGE) ;
  • Han, Xiaosen (COLLEGE OF MATHEMATICS AND INFORMATION SCIENCE HENAN UNIVERSITY)
  • Published : 2009.05.31
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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.

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References

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