Nonuniqueness of phase transitions near the Maxwell line
HTML articles powered by AMS MathViewer
- by S. Benzoni-Gavage
- Proc. Amer. Math. Soc. 127 (1999), 1183-1190
- DOI: https://doi.org/10.1090/S0002-9939-99-04719-X
- PDF | Request permission
Abstract:
We consider the description of propagating phase boundaries in a van der Waals fluid by means of viscocapillary profiles, which are viewed as heteroclinic orbits connecting nonhyperbolic fixed points of a five dimensional dynamical system. A bifurcation analysis enables us to show that, for small viscosities, some distinct propagating phase boundaries share the same metastable state on one side of the front.References
- S. Benzoni-Gavage, Stability of multidimensional phase transitions. Nonlinear Analysis T.M.A., 31, no. 1/2 (1998), pp. 243-263.
- Hai Tao Fan and Marshall Slemrod, The Riemann problem for systems of conservation laws of mixed type, Shock induced transitions and phase structures in general media, IMA Vol. Math. Appl., vol. 52, Springer, New York, 1993, pp. 61–91. MR 1240333, DOI 10.1007/978-1-4613-8348-2_{4}
- H. Freistühler, The persistence of ideal shock waves, Appl. Math. Lett. 7 (1994), no. 6, 7–11. MR 1340723, DOI 10.1016/0893-9659(94)90085-X
- Michael Grinfeld, Dynamic phase transitions: existence of “cavitation” waves, Proc. Roy. Soc. Edinburgh Sect. A 107 (1987), no. 1-2, 153–163. MR 918899, DOI 10.1017/S0308210500029413
- D. Serre, Systems of conservation laws. Cambridge University Press, to appear.
- 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 10.1007/BF00250857
- 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 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 10.1007/BF00250844
Bibliographic Information
- S. Benzoni-Gavage
- Affiliation: CNRS-ENS Lyon, UMR 128, 46, allée d’Italie, F-69364 Lyon Cedex 07, France
- Email: benzoni@umpa.ens-lyon.fr
- Received by editor(s): July 16, 1997
- Communicated by: Jeffrey Rauch
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1183-1190
- MSC (1991): Primary 76T05, 35M10, 34C37; Secondary 35L67, 58F14
- DOI: https://doi.org/10.1090/S0002-9939-99-04719-X
- MathSciNet review: 1485459