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Dynamic phase transitions: Existence of “cavitation” waves

Published online by Cambridge University Press:  14 November 2011

Michael Grinfeld
Michael Grinfeld
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, U.K.
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Synopsis

In this paper we examine the influence of capillarity on existence and uniqueness of travelling wave solutions in an isothermal system of van der Waals fluids. Existence and non-uniqueness theorems are proved using phase-space analysis and topological methods.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 107 , Issue 1-2 , 1987 , pp. 153 - 163
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Conley, C.. Isolated Invariant Sets and the Morse Index. CBMS Publications No. 38 (Providence, R.I.: American Mathematical Society, 1978).CrossRefGoogle Scholar
2Dunbar, S. R.. Traveling wave solutions of diffusive Lotka-Volterra interaction equations (Ph.D. Thesis, University of Minnesota, Minneapolis, 1981).Google Scholar
3Dettleff, G., Thompson, P. A., Meier, G. E. A. and Speckmann, H.-D.. An experimental study of liquefaction shock waves. J. Fluid Mech. 95 (1979), 279–304.CrossRefGoogle Scholar
4Grinfeld, M.. Topological techniques in dynamic phase transitions (Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, N.Y., 1986).Google Scholar
5Grinfeld, M.. Non-isothermal dynamic phase transitions (in prep.).Google Scholar
6Hagan, R.. Dynamic phase transitions (Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, N.Y., 1982).Google Scholar
7Mischaikov, K.. Classification of traveling wave solutions of reaction-diffusion equations (Brown University LCDS Preprint 86–5, 1985).CrossRefGoogle Scholar
8Shearer, M.. Admissibility criteria for shock wave solutions of a system of conservation laws of mixed type. Proc. Roy. Soc. Edinburgh Sect. A. 93 (1983), 233–244.CrossRefGoogle Scholar
9Slemrod, M.. Admissibility criteria for propagating phase boundaries in a van der Waals fluid. Arch. Rational Mech. Anal. 81 (1983), 301–316.CrossRefGoogle Scholar
10Slemrod, M.. Dynamics of first order phase transitions. In Phase Transformations and Material Instabilities in Solids, ed. Gurtin, M. E., pp. 163–204 (New York: Academic Press, 1984).Google Scholar
11Slemrod, M.. Dynamic phase transitions in a van der Waals fluid. J. Differential Equations 52 (1984), 1–23.CrossRefGoogle Scholar
12Terman, D.. Traveling wave solutions of multistable reaction-diffusion equations. In Nonlinear Partial Differential Equations, ed. Smoller, J. A., pp. 361–378 (Providence, R.I.: American Mathematical Society, 1983).CrossRefGoogle Scholar