The uniqueness and stability of the solution of the Riemann problem of a system of conservation laws of mixed type
Author:
Hai Tao Fan
Journal:
Trans. Amer. Math. Soc. 333 (1992), 913938
MSC:
Primary 35L65; Secondary 76L05
MathSciNet review:
1104200
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Abstract: We establish the uniqueness and stability of the similarity solution of the Riemann problem for a system of conservation laws of mixed type, with initial data separated by the elliptic region, which satisfies the viscositycapillarity travelling wave admissibility criterion.
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 , Solution of the Riemann problem for a class of hyperbolic conservation laws by the viscosity method, Arch. Rational Mech. Anal. 52 (1973), 19. MR 0340837 (49:5587)
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 [5]
 C. M. Dafermos, Admissible wave fans in nonlinear hyperbolic systems, Arch. Rational Mech. Anal. 106 (1989), 243360. MR 981663 (90m:35124)
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 Haitao Fan, The structure of the solutions of the gas dynamics equation and the formation of the vacuum state, Quart. Appl. Math., (to appear). MR 1096230 (92e:76053)
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 H.T. Fan, A limiting "viscosity" approach to the Riemann problem for the materials exhibiting change of phase. II, Arch. Rational Mech. Anal, (to appear). MR 1132765 (93a:35102)
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 T.P. Liu, The Riemann problem for general system of conservation laws, J. Differential Equations 18 (1975), 218234. MR 0369939 (51:6168)
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 M. Shearer, Riemann problem for a class of conservation laws of mixed type, J. Differential Equations 46 (1982), 426443. MR 681232 (84a:35164)
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 M. Slemrod and A. Tzavaras, A limiting viscosity approach for the Riemann problem in isentropic gas dynamics, Indiana Univ. Math. J. (submitted).
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199211042007
PII:
S 00029947(1992)11042007
Keywords:
Viscositycapillarity travelling wave criterion
Article copyright:
© Copyright 1992
American Mathematical Society
