Riemann problem for hyperbolic systems of conservation laws with no classical wave solutions
Author:
De Chun Tan
Journal:
Quart. Appl. Math. 51 (1993), 765-776
MSC:
Primary 35L65; Secondary 35L67, 76L05
DOI:
https://doi.org/10.1090/qam/1247440
MathSciNet review:
MR1247440
Full-text PDF Free Access
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Additional Information
- Constantine M. Dafermos, Solution of the Riemann problem for a class of hyperbolic systems of conservation laws by the viscosity method, Arch. Rational Mech. Anal. 52 (1973), 1–9. MR 340837, DOI https://doi.org/10.1007/BF00249087
- C. M. Dafermos and R. J. DiPerna, The Riemann problem for certain classes of hyperbolic systems of conservation laws, J. Differential Equations 20 (1976), no. 1, 90–114. MR 404871, DOI https://doi.org/10.1016/0022-0396%2876%2990098-X
- Philippe LeFloch, Entropy weak solutions to nonlinear hyperbolic systems under nonconservative form, Comm. Partial Differential Equations 13 (1988), no. 6, 669–727. MR 934378, DOI https://doi.org/10.1080/03605308808820557
- Philippe LeFloch, An existence and uniqueness result for two nonstrictly hyperbolic systems, Nonlinear evolution equations that change type, IMA Vol. Math. Appl., vol. 27, Springer, New York, 1990, pp. 126–138. MR 1074190, DOI https://doi.org/10.1007/978-1-4613-9049-7_10
- David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin-New York, 1977. Grundlehren der Mathematischen Wissenschaften, Vol. 224. MR 0473443
- James Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18 (1965), 697–715. MR 194770, DOI https://doi.org/10.1002/cpa.3160180408
- Barbara Lee Keyfitz and Herbert C. Kranzer, A viscosity approximation to a system of conservation laws with no classical Riemann solution, Nonlinear hyperbolic problems (Bordeaux, 1988) Lecture Notes in Math., vol. 1402, Springer, Berlin, 1989, pp. 185–197. MR 1033283, DOI https://doi.org/10.1007/BFb0083875
- Dennis James Korchinski, SOLUTION OF A RIEMANN PROBLEM FOR A 2 X 2 SYSTEM OF CONSERVATION LAWS POSSESSING NO CLASSICAL WEAK SOLUTION, ProQuest LLC, Ann Arbor, MI, 1977. Thesis (Ph.D.)–Adelphi University. MR 2626928
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- Tai Ping Liu, The Riemann problem for general systems of conservation laws, J. Differential Equations 18 (1975), 218–234. MR 369939, DOI https://doi.org/10.1016/0022-0396%2875%2990091-1
- Tong Chang and De Chun Tan, Two-dimensional Riemann problem for a hyperbolic system of conservation laws, Acta Math. Sci. (English Ed.) 11 (1991), no. 4, 369–392. MR 1174368, DOI https://doi.org/10.1016/S0252-9602%2818%2930255-8
A. I. Volpert, The space BV and quasilinear equations, Math. USSR-Sb. 2, 257–267 (1967)
C. M. Dafermos, Solution of the Riemann problem for a class of hyperbolic systems of conservation laws by the viscosity method, Arch. Rational Mech. Anal. 52, 1–9 (1973)
C. M. Dafermos and R. J. DiPerna, The Riemann problem for certain classes of hyperbolic systems of conservation laws, J. Differential Equations 20, 90–114 (1976)
P. Le Floch, Entropy weak solutions to nonlinear hyperbolic systems under nonconservative form, Comm. Partial Differential Equations 13 (6), 669–727 (1988)
---, An existence and uniqueness result for two nonstrictly hyperbolic systems, Nonlinear Evolution Equations that Change Type (Keyfitz and Shearer, eds.), IMA series, vol. 27, Springer, New York, 1990, pp. 126–138
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin and New York, 1977
J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18, 697–715 (1965)
B. L. Keyfitz and H. C. Kranzer, A viscosity approximation to a system of conservation laws with no classical Riemann solution, Nonlinear Hyperbolic Problems, Lecture Notes in Math., no. 1402, Springer-Verlag, Berlin and New York, 1989, pp. 185–197
D. J. Korchinski, Solution of a Riemann problem for a $2 \times 2$ system of conservation laws possessing no classical weak solution, Ph.D. Thesis, Adelphi University, Garden City, New York, 1977
P. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 10, 537–556 (1957)
T.-P. Liu, The Riemann problem for general systems of conservation laws, J. Differential Equations 18, 218–234 (1975)
D. C. Tan, T. Zhang, and Y. Z. Zheng, Delta-shock wave solutions for hyperbolic systems of conservation laws, submitted to J. Differential Equations
A. I. Volpert, The space BV and quasilinear equations, Math. USSR-Sb. 2, 257–267 (1967)
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Article copyright:
© Copyright 1993
American Mathematical Society
