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. 
View via Publisher
ndsl.kr
8 Citations
Background Citations
1
Methods Citations
1

Figures from this paper

8 Citations

Citation Type

Citation Type

The Generalized Riemann Problem for First Order Quasilinear Hyperbolic Systems of Conservation Laws II
  • 4
Generalized Riemann problems and exact solutions for p-systems with relaxation
  • 11
A reduction procedure for generalized Riemann problems with application to nonlinear transmission lines
  • 46
A Well-Balanced Finite Volume Scheme for a Mixed Hyperbolic/Parabolic System to Model Chemotaxis
  • 6
  • PDF
Approximate solutions of generalized Riemann problems for nonlinear systems of hyperbolic conservation laws
  • 15
  • PDF
Riemann problems and exact solutions to a traffic flow model
  • 19
Approximate solutions of generalized Riemann problems: The Toro-Titarev solver and the LeFloch-Raviart expansion
  • 4
  • PDF
An admissibility and asymptotic preserving scheme for systems of conservation laws with source term on 2D unstructured meshes with high-order MOOD reconstruction
  • 5
  • PDF

References

SHOWING 1-10 OF 11 REFERENCES
The Generalized Riemann Problem for Quasilinear Hyperbolic Systems of Conservation Laws
  • 6
LOCAL SOLVABILITY OF THE BOUNDARY VALUE PROBLEMS FOR QUASILINEAR HYPERBOLIC SYSTEMS
  • 8
Hyberbolic [i.e. Hyperbolic] conservation laws in continuum physics
  • 636
Shock Waves and Reaction-Diffusion Equations
  • 3,630
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
...
1
2
...