Archive for Rational Mechanics and Analysis

, Volume 116, Issue 4, pp 317–337

A limiting “viscosity” approach to the Riemann problem for materials exhibiting a change of phase(II)

  • Haitao Fan


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. D. James, The propagation of phase boundaries in elastic bars, Arch. Rational Mech. Anal. 73 (1980) 125–158.Google Scholar
  2. 2.
    M. Shearer, Riemann problem for a class of conservation laws of mixed type, J. Diff. Eqs. 46 (1982) 426–443.Google Scholar
  3. 3.
    M. Shearer, Nonuniqueness of admissible solutions of Riemann initial value problems for a system of conservation laws of mixed type, Arch. Rational Mech. Anal. 93 (1986) 45–59.Google Scholar
  4. 4.
    M. Shearer, Dynamic phase transitions in a van der Waals gas, Quart. Appl. Math., 46 (1988) 631–636.Google Scholar
  5. 5.
    L. Hsiao, Admissibility criterion and admissible weak solutions of Riemann problem for conservation laws of mixed type, Workshop Proceedings on Nonlinear Evolution Equations that Change Type, to appear in IMA Volumes in Mathematics and its Applications.Google Scholar
  6. 6.
    J. Glimm, The interactions of nonlinear hyperbolic waves, Comm. Pure Appl. Math. 41 (1988) 569–590.Google Scholar
  7. 7.
    M. Slemrod, A limiting “viscosity” approach to the Riemann problem for materials exhibiting change of phase, Arch. Rational Mech. Anal. 105 (1989) 327–365.Google Scholar
  8. 8.
    A. S. Kalašnikov, construction of generalized solutions of quasi-linear equations of first order without convexity conditions as limits of solutions of parabolic equations with a small parameter, Dokl. Akad. Nauk. SSSR 127 (1959) 27–30.Google Scholar
  9. 9.
    V. A. Tupčiev, The asymptotic behavior of the solutions of Cauchy problem for the equation ɛ 2 tu xx=ut+[φ(u)]xthat degenerates for ξ=0 into the problem of the decay of an arbitrary discontinuity for the case of a rarefaction wave, Z. Vyčisl. Mat. Fis. 12 (1972) 770–775; English translation in USSR Comput. Math. Phys. 12.Google Scholar
  10. 10.
    V. A. Tupčiev, On the method of introducing viscosity in the study of problems involving the decay of discontinuity, Dokl. Akad. Nauk. SSSR 211 (1973) 55–58.Google Scholar
  11. 11.
    C. M. Dafermos, Solutions of the Riemann problem for a class of hyperbolic conservation laws by the viscosity method, Arch. Rational Mech. Anal. 52 (1973) 1–9.Google Scholar
  12. 12.
    C. M. Dafermos, Structure of the solutions of the Riemann problem for hyperbolic conservation laws, Arch. Rational Mech. Anal. 53 (1974) 203–217.Google Scholar
  13. 13.
    C. M. Dafermos, Admissible wave fans in nonlinear hyperbolic system, Arch. Rational Mech. Anal. 106 (1989) 243–260.Google Scholar
  14. 14.
    C. M. Dafermos & R. J. DiPerna, The Riemann problem for certain classes of hyperbolic systems of conservation laws, J. Diff. Eqs. 20 (1976) 90–114.Google Scholar
  15. 15.
    M. Slemrod & A. Tzavaras, A limiting viscosity approach for the Riemann problem in isentropic gas dynamics, Indiana Univ. Math. J. 38 1989 1047–1074.Google Scholar
  16. 16.
    Haitao Fan, The structure of the solutions of the gas dynamics equation and the formation of the vacuum state, submitted to Quart. Appl. Math. Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Haitao Fan
    • 1
  1. 1.Department of MathematicsUniversity of WisconsinMadison

Personalised recommendations