Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
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  • [1] 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) MR 0340837
  • [2] 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) MR 0404871
  • [3] 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) MR 1218743
  • [4] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer-Verlag, 1983 MR 737190
  • [5] 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 MR 1033283
  • [6] 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 MR 2626928
  • [7] M. Slemrod, A limiting ``viscosity'' approach to the Riemann problem for materials exhibiting change of phase, Arch. Rat. Mech. Anal. 41, 327-366 (1989) MR 973246
  • [8] 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) MR 1029688
  • [9] 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 MR 0330801
  • [10] 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) MR 1174368
  • [11] 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) MR 1287550

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DOI: https://doi.org/10.1090/qam/1447583
Article copyright: © Copyright 1997 American Mathematical Society

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