Article PDF
Avoid common mistakes on your manuscript.
References
Liebovich, L., Solutions of the Riemann problem for hyperbolic systems of quasilinear equations without convexity conditions. J. Math. Appl. 45 (1974), 81–90.
Liu, T. P., The Riemann problem for general 2×2 conservation laws. Trans. Amer. Math. Soc. 199 (1974), 89–112.
Lax, P. D., Hyperbolic systems of conservation laws and the mathematical theory of shock waves, CBMS Regional Conference Series in Applied Mathematics, SIAM Publications: Philadelphia (1973).
Wendroff, B., The Riemann problem for materials with nonconvex equations of state, I: Isentropic Flow. J. Math. Anal. Appl. 38 (1972), 454–466.
Dafermos, C. M., The entropy rate admissibility criterion for solutions of hyperbolic conservation laws. J. Differential Equations 14 (1973), 202–212.
Dafermos, C. M., The entropy rate admissibility criterion in thermoelasticity. Rendiconti della Classe di Science Fisiche, Matematiche e Naturali Accademia del Lincei, (7) 57 (1974), 113–119.
James, R. D., The propagation of phase boundaries in elastic bars. Arch. Rational Mech. Anal. 73 (1980), 125–158.
Shearer, M., The Riemann problem for a class of conservation laws of mixed type. J. Differential Equations 46 (1982), 426–443.
Slemrod, M., Admissibility criteria for propagating phase boundaries in a van der Waals fluid. Arch. Rational Mech. Anal. 81 (1983), 301–315.
Greenberg, J. M., On the elementary interactions for the quasilinear wave equation. Arch. Rational Mech. Anal. 43 (1971), 325–349.
Author information
Authors and Affiliations
Additional information
Communicated by C. M. Dafermos
Rights and permissions
About this article
Cite this article
Hattori, H. The Riemann problem for a van der Waals fluid with entropy rate admissibility criterion — Isothermal case. Arch. Rational Mech. Anal. 92, 247–263 (1986). https://doi.org/10.1007/BF00254828
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00254828