The Riemann problem for general conservation laws

Author:
Tai Ping Liu

Journal:
Trans. Amer. Math. Soc. **199** (1974), 89-112

MSC:
Primary 35L65

DOI:
https://doi.org/10.1090/S0002-9947-1974-0367472-1

MathSciNet review:
0367472

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Abstract | References | Similar Articles | Additional Information

Abstract: The Riemann Problem for a system of hyperbolic conservation laws of form

**[1]**J. Glimm,*Solution in the large for nonlinear hyperbolic systems of equations*, Comm. Pure Appl. Math.**18**(1965), 697-715. MR**33**#2976. MR**0194770 (33:2976)****[2]**J. A. Smoller and J. L. Johnson,*Global solutions for an extended class of hyperbolic systems of conservation laws*, Arch. Rational Mech. Anal.**32**(1969), 169-189. MR**38**#4822. MR**0236527 (38:4822)****[3]**P. D. Lax,*Hyperbolic systems of conservation laws*. II, Comm. Pure Appl. Math.**10**(1957), 537-566. MR**20**#176. MR**0093653 (20:176)****[4]**T. Nishida,*Global solution for an initial boundary value problem of a quasilinear hyperbolic system*, Proc. Japan Acad.**44**(1968), 642-646. MR**38**#4821. MR**0236526 (38:4821)****[5]**T. Nishida and J. A. Smoller,*Solution in the large for some nonlinear hyperbolic conservation laws*, Comm. Pure Appl. Math.**25**(1973), 183-200. MR**0330789 (48:9126)****[6]**O. A. Oleĭnik,*On the uniqueness of the generalized solution of Cauchy problem for nonlinear system of equations occuring in mechanics*, Uspehi Mat. Nauk**12**(1957), no. 6 (78), 169-176. (Russian) MR**20**#1057. MR**0094543 (20:1057)****[7]**J. A. Smoller,*On the solution of the Riemann problem with general step data for an extended class of hyperbolic systems*, Michigan Math. J.**16**(1969), 201-210. MR**40**#552. MR**0247283 (40:552)****[8]**-,*A uniqueness theorem for Riemann problems*, Arch. Rational Mech. Anal.**33**(1969), 110-115. MR**38**#6238. MR**0237961 (38:6238)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0367472-1

Keywords:
Conservation laws,
shocks ,
rarefaction waves ,
contact discontinuities,
Oleinik condition (E),
Lax shock inequalities (L),
shock speed

Article copyright:
© Copyright 1974
American Mathematical Society