Dynamic phase transitions in a van der Waals gas

Shearer, Michael

doi:10.1090/qam/973380

Author: Michael Shearer
Journal: Quart. Appl. Math. 46 (1988), 631-636
MSC: Primary 76L05; Secondary 76N15
DOI: https://doi.org/10.1090/qam/973380
MathSciNet review: 973380
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Harumi Hattori, The entropy rate admissibility criterion and the double phase boundary problem, Nonstrictly hyperbolic conservation laws (Anaheim, Calif., 1985) Contemp. Math., vol. 60, Amer. Math. Soc., Providence, RI, 1987, pp. 51–65. MR 873531, DOI https://doi.org/10.1090/conm/060/873531
Richard D. James, The propagation of phase boundaries in elastic bars, Arch. Rational Mech. Anal. 73 (1980), no. 2, 125–158. MR 556559, DOI https://doi.org/10.1007/BF00258234
P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 10 (1957), 537–566. MR 93653, DOI https://doi.org/10.1002/cpa.3160100406
Tai Ping Liu, The Riemann problem for general $2\times 2$ conservation laws, Trans. Amer. Math. Soc. 199 (1974), 89–112. MR 367472, DOI https://doi.org/10.1090/S0002-9947-1974-0367472-1
Robert L. Pego, Phase transitions in one-dimensional nonlinear viscoelasticity: admissibility and stability, Arch. Rational Mech. Anal. 97 (1987), no. 4, 353–394. MR 865845, DOI https://doi.org/10.1007/BF00280411
David G. Schaeffer and Michael Shearer, The classification of $2\times 2$ systems of nonstrictly hyperbolic conservation laws, with application to oil recovery, Comm. Pure Appl. Math. 40 (1987), no. 2, 141–178. MR 872382, DOI https://doi.org/10.1002/cpa.3160400202
Michael Shearer, Admissibility criteria for shock wave solutions of a system of conservation laws of mixed type, Proc. Roy. Soc. Edinburgh Sect. A 93 (1982/83), no. 3-4, 233–244. MR 688788, DOI https://doi.org/10.1017/S0308210500015948
Michael 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), no. 1, 45–59. MR 822335, DOI https://doi.org/10.1007/BF00250844
Michael Shearer, The Riemann problem for a class of conservation laws of mixed type, J. Differential Equations 46 (1982), no. 3, 426–443. MR 681232, DOI https://doi.org/10.1016/0022-0396%2882%2990103-6
M. Shearer, D. G. Schaeffer, D. Marchesin, and P. L. Paes-Leme, Solution of the Riemann problem for a prototype $2\times 2$ system of nonstrictly hyperbolic conservation laws, Arch. Rational Mech. Anal. 97 (1987), no. 4, 299–320. MR 865843, DOI https://doi.org/10.1007/BF00280409
M. Slemrod, Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. Rational Mech. Anal. 81 (1983), no. 4, 301–315. MR 683192, DOI https://doi.org/10.1007/BF00250857
Burton Wendroff, The Riemann problem for materials with nonconvex equations of state. I. Isentropic flow, J. Math. Anal. Appl. 38 (1972), 454–466. MR 328387, DOI https://doi.org/10.1016/0022-247X%2872%2990103-5