Nonuniqueness of phase transitions

near the Maxwell line

Author:
S. Benzoni-Gavage

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

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Abstract | References | Similar Articles | Additional Information

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.

**1.**S. Benzoni-Gavage,*Stability of multidimensional phase transitions.*Nonlinear Analysis T.M.A.,**31**, no. 1/2 (1998), pp. 243-263. CMP**98:06****2.**H. Fan & M. Slemrod,*The Riemann problem for systems of conservation laws of mixed type.*IMA Vol. Math. Appl.,**52**(1993), pp. 61-91. MR**94h:35152****3.**H. Freistühler,*The Persistence of Ideal Shock Waves.*Appl. Math. Lett.,**7**no 6 (1994), pp. 7-11. MR**96c:35114****4.**M. Grinfeld,*Dynamic phase transitions: Existence of ``cavitation waves''.*Proc. Roy. Soc. Edinburgh Sect. A,**107**(1987), pp. 153-163. MR**88k:35123****5.**D. Serre,*Systems of conservation laws.*Cambridge University Press, to appear.**6.**M. Slemrod,*Admissibility criteria for propagating phase boundaries in a van der Waals fluid.*Arch. Rational Mech. Anal.**81**(1983), pp. 301-315. MR**84a:76030****7.**M. Shearer,*Admissibility criteria for shock wave solutions of a system of conservation laws of mixed type.*Proc. Roy. Soc. Edinburgh**93 A**(1983), pp. 233-244. MR**84c:35075****8.**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), pp. 45-59. MR**87h:35207**

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Additional 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

DOI:
https://doi.org/10.1090/S0002-9939-99-04719-X

Keywords:
Phase transitions,
profiles,
heteroclinic orbits

Received by editor(s):
July 16, 1997

Communicated by:
Jeffrey Rauch

Article copyright:
© Copyright 1999
American Mathematical Society