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

@article{Chen2009THEGR,
  title={THE GENERALIZED RIEMANN PROBLEM FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS I},
  author={S. Chen and D. Huang and X. Han},
  journal={Bulletin of The Korean Mathematical Society},
  year={2009},
  volume={46},
  pages={409-434}
}
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. 
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SHOWING 1-10 OF 11 REFERENCES
The Generalized Riemann Problem for Quasilinear Hyperbolic Systems of Conservation Laws
  • 6
Hyberbolic [i.e. Hyperbolic] conservation laws in continuum physics
  • 636
Shock Waves and Reaction-Diffusion Equations
  • 3,631
Hyperbolic systems of conservation laws
  • 664
The regularity of solution for first order quasilinear hyperbolic systems
  • Chin. Ann. Math. 6A
  • 1985
A boundary value problem for hyperbolic systems and its applications
  • Acta Math. Sinica 13
  • 1963
The Cauchy problem of hyperbolic systems with discontinuous initial values
  • Collections of Scientific and Technological Papers, Shanghai, Mathematics Chemistry Edition
  • 1960
The Cauchy problem of typical hyperbolic systems with discontinuous initial values, Collections of Mathematical Papers of Fudan University
  • 1960
Hyperbolic systems of conservation laws II
  • 2,466
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