Nonisothermal dynamic phase transitions
Author:
Michael Grinfeld
Journal:
Quart. Appl. Math. 47 (1989), 71-84
MSC:
Primary 35Q20; Secondary 58F07, 76T05, 80A99
DOI:
https://doi.org/10.1090/qam/987896
MathSciNet review:
987896
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: In this work we prove existence of travelling wave solutions to the Korteweg theory of capillarity regularization of conservation laws governing the motion of a van der Waals fluid. These solutions connect states in different phases and thus can be interpreted as dynamic phase transitions.
- C. C. Conley, Some abstract properties of the set of invariant sets of a flow, Illinois J. Math. 16 (1972), 663–668. MR 315686
- C. Conley and R. Gardner, An application of the generalized Morse index to travelling wave solutions of a competitive reaction-diffusion model, Indiana Univ. Math. J. 33 (1984), no. 3, 319–343. MR 740953, DOI https://doi.org/10.1512/iumj.1984.33.33018
- C. Conley and Joel Smoller, Isolated invariant sets of parameterized systems of differential equations, The structure of attractors in dynamical systems (Proc. Conf., North Dakota State Univ., Fargo, N.D., 1977) Lecture Notes in Math., vol. 668, Springer, Berlin, 1978, pp. 30–47. MR 518546
G. Detleff, P. A. Thompson, G. E. A. Meier, and H.-D. Speckmann, An experimental study of liquefaction shock waves, J. Fluid Mech. 95, 279–304 (1979)
M. Grinfeld, Topological techniques in dynamic phase transitions, Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, N.Y. (1986)
- 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 https://doi.org/10.1017/S0308210500029413
- 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
- M. Slemrod, Dynamics of first order phase transitions, Phase transformations and material instabilities in solids (Madison, Wis., 1983) Publ. Math. Res. Center Univ. Wisconsin, vol. 52, Academic Press, Orlando, FL, 1984, pp. 163–203. MR 802225
- M. Slemrod, Dynamic phase transitions in a van der Waals fluid, J. Differential Equations 52 (1984), no. 1, 1–23. MR 737959, DOI https://doi.org/10.1016/0022-0396%2884%2990130-X
- Joel Smoller, Shock waves and reaction-diffusion equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 258, Springer-Verlag, New York-Berlin, 1983. MR 688146
C. Conley, Some abstract properties of the set of invariant sets of a flow, Illinois J. Math. 16, 663–668 (1972)
C. Conley and R. Gardner, An application of the generalized Morse index to travelling wave solutions of a competitive reaction-diffusion model, Indiana Univ. Math. J. 33, 319–342 (1984)
C. Conley and J. Smoller, Isolated invariant sets of parametrized systems of differential equations, in The structure of attractors in dynamical systems, N. G. Markley, J. C. Martin, and W. Perizzo (eds.), Lecture Notes in Math. 668, Springer-Verlag, 1978
G. Detleff, P. A. Thompson, G. E. A. Meier, and H.-D. Speckmann, An experimental study of liquefaction shock waves, J. Fluid Mech. 95, 279–304 (1979)
M. Grinfeld, Topological techniques in dynamic phase transitions, Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, N.Y. (1986)
M. Grinfeld, Isothermal dynamic phase transitions: existence of “cavitation waves", Proc. Roy. Soc. Edinburgh Sect. A, 107A, 153–163 (1987)
M. Slemrod, Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. Rat. Mech. Anal. 81, 301–316 (1983)
M. Slemrod, Dynamics of first order phase transitions, in Phase transformations and material instabilities in solids, M. E. Gurtin (ed.), Academic Press, New York, 1984
M. Slemrod, Dynamic phase transitions in a van der Waals fluid, J. Differential Equations 52, 1–23 (1984)
J. Smoller, Shock waves and reaction-diffusion equations, Springer-Verlag, New York, 1983
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
35Q20,
58F07,
76T05,
80A99
Retrieve articles in all journals
with MSC:
35Q20,
58F07,
76T05,
80A99
Additional Information
Article copyright:
© Copyright 1989
American Mathematical Society
