A limiting viscosity approach to Riemann solutions containing delta-shock waves for nonstrictly hyperbolic conservation laws
Author:
Jiaxin Hu
Journal:
Quart. Appl. Math. 55 (1997), 361-373
MSC:
Primary 35L65; Secondary 35D05
DOI:
https://doi.org/10.1090/qam/1447583
MathSciNet review:
MR1447583
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
- Hai Tao Fan, A vanishing viscosity approach on the dynamics of phase transitions in van der Waals fluids, J. Differential Equations 103 (1993), no. 1, 179–204. MR 1218743, DOI https://doi.org/10.1006/jdeq.1993.1046
- David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983. MR 737190
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- 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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- De Chun Tan, Tong Zhang, and Yu Xi Zheng, Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws, J. Differential Equations 112 (1994), no. 1, 1–32. MR 1287550, DOI https://doi.org/10.1006/jdeq.1994.1093
C. M. Dafermos, Solution of the Riemann problem for a class of hyperbolic systems of conservation laws by the viscosity method, Arch. Rat. 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)
H. T. Fan, A vanishing viscosity approach on the dynamics of phase transitions in van der Waals fluids, J. Differential Equations 103, 179–204 (1993)
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer-Verlag, 1983
B. L. Keyfitz and H. C. Kranzer, A viscosity approximation to system of conservation laws with no classical Riemann solutions, Nonlinear Hyperbolic Problem, Lecture Notes in Math., Vol. 1402, Springer-Verlag, NY, 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, 1977
M. Slemrod, A limiting “viscosity” approach to the Riemann problem for materials exhibiting change of phase, Arch. Rat. Mech. Anal. 41, 327–366 (1989)
M. Slemrod and A. E. Tzavaras, A limiting viscosity approach for the Riemann problem in isentropic gas dynamics, Indiana Univ. Math. J. 4, 1047–1074 (1989)
V. A. Tupciev, On the method of introducing viscosity in the study of problems involving decay of a discontinuity, Dokl. Akad. Nauk SSR 211, 55–58 (1973); translated in Soviet Math. Dokl. 14
D. C. Tan and T. Zhang, Two-dimensional Riemann problem for a hyperbolic system on nonlinear conservation laws, Acta Math. Sci. 11, 369–392 (1991)
D. C. Tan, T. Zhang, and Y. X. Zheng, Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws, J. Differential Equations 112, 1–32 (1994)
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© Copyright 1997
American Mathematical Society
