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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References | Similar Articles | Additional Information

**[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**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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Additional Information

DOI:
https://doi.org/10.1090/qam/1447583

Article copyright:
© Copyright 1997
American Mathematical Society