# THE RIEMANN PROBLEM FOR A SYSTEM OF CONSERVATION LAWS OF MIXED TYPE (I)

• Choon-Ho Lee
• Published : 1998.02.01
• 31 2

#### Abstract

We prove the existence of solutions of the Reimann problem for a system of conservation laws of mixed type using the method of vanishing viscosity term.

#### Keywords

Riemann problem;existence of solutions;fixed point theorem

#### References

1. Arch. Rational Mech. Anal. v.52 Solutions of the Ricmann Problem Problem for a Class of Hyperbolic Systems of Conservation laws by Viscosity method C.M. Dagermos
2. Arch. Rational Mech. Anal. v.105 A Limiting "Viscosity" Approach to the Riemann problem for materials Exhibiting Change of Phase M. Slemrod
3. Dokl. Akad. Nauk. SSSR v.211 On the method of introducing viscosity in the study of problems involving decay of a discontinuity V.A. Tupciev
4. Dokl. Akad. Nauk. SSSR v.127 Construction of generalized solutions of quasilinear equations of first order without convexity conditions as limits of solutions of parabolic equations with a small parameter A.S. Kalashnikov
5. Z. Vycisl. Mat. Fiz. v.12 The asymptotic behavior of the solution of the Cauchy problem for the equation $ε^2tu_{xx}=u_t+[Φ(α)]_x$ that degenerates for ε=0 into the problem of the decay of an arbitrary discontinuity for the case of a rarefaction wave V.A. Tupciev
6. English transl. in Soviet Math. v.14
7. Arch. Rational Mech. Anal. A limiting "Viscosity" approach to the Riemann problem for materials exhibiting a change of phase (Ⅱ) H. Fan
8. English transl. in USSR comput. Math. and Phys. v.12
9. J. Diff. Equat. v.20 The Riemann problem for certain classes of hyperbolic systems of conservation laws C.M. Dagermos;R.J. DiPerna
10. Arch. Rational Mech. Anal. v.73 The propagation of phase boundaries in elastic bars R.D. James