Delta-shock waves as self-similar viscosity limits
Author:
Grey Ercole
Journal:
Quart. Appl. Math. 58 (2000), 177-199
MSC:
Primary 35L67; Secondary 35L65
DOI:
https://doi.org/10.1090/qam/1739044
MathSciNet review:
MR1739044
Full-text PDF Free Access
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- 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 limiting “viscosity” approach to the Riemann problem for materials exhibiting a change of phase. II, Arch. Rational Mech. Anal. 116 (1992), no. 4, 317–337. MR 1132765, DOI https://doi.org/10.1007/BF00375671
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- M. Slemrod, A limiting “viscosity” approach to the Riemann problem for materials exhibiting change of phase, Arch. Rational Mech. Anal. 105 (1989), no. 4, 327–365. MR 973246, DOI https://doi.org/10.1007/BF00281495
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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 limiting viscosity approach to the Riemann problem for materials exhibiting change of phase II, Arch. Rat. Mech. Anal. 116, 317–338 (1992)
H. T. Fan, One-phase Riemann problem and wave interactions in systems of conservation laws of mixed type, SIAM J. Math. Anal. (4) 24, 840–865 (1993)
J. Hu, A limiting viscosity approach to Riemann solutions containing delta-shock waves for non-strictly hyperbolic conservation laws, Quart. Appl. Math. (2) 55, 361–373 (1997)
F. Huang, Existence and uniqueness of discontinuous solutions for a hyperbolic system, Proc. Roy. Soc. Edinburgh 127, 1193–1205 (1997)
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., Vol. 1402, Springer-Verlag, NY, 1989, pp. 185–197
B. L. Keyfitz and H. C. Kranzer, A strictly hyperbolic system of conservation laws admitting singular shocks, in Nonlinear Evolution Equations that Change Type, IMA Vol. Math. Appl. 27, 107–125 (1990)
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. 105, 327–365 (1989)
M. Slemrod and A. E. Tzavaras, A limiting viscosity approach for the Riemann problem in isentropic gas dynamics, Indiana Univ. Math. J. (4) 38, 1047–1074 (1989)
D. Tan, Riemann problem for hyperbolic systems of conservation laws with no classical wave solutions, Quart. Appl. Math. (4) 51, 765–776 (1993)
D. Tan, T. Zhang, and Y. Zheng, Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws, J. Differential Equations 112, 1–32 (1994)
A. E. Tzavaras, Elastic as limit of viscoelastic response, in a context of self-similar viscous limits, J. Differential Equations 123, 305–341 (1995)
A. E. Tzavaras, Wave interactions and variation estimates for self-similar zero-viscosity limits in systems of conservation laws, Arch. Rational Mech. Anal. 135, 1–60 (1996)
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