Front motion for phase transitions in systems with memory

Physica D: Nonlinear Phenomena

Volumn 146, Issue 1-4, 2000, Pages 137-149

  Rotstein, Horacio G ^a   Domoshnitsky, Alexander I ^b   Nepomnyashchy, Alexander ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b ARIEL UNIVERSITY   (Israel)

Author keywords

Allen Cahn equation memory; Born Infeld equation; Front motion; Integro differential equations; Phase transition dynamics with memory

Indexed keywords

EID: 0001551977     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(00)00132-9     Document Type: Article

References (21)

1. Caginalp G. An analysis of a phase field model of a free boundary. Arch. Rat. Mech. Anal. 92:1986;205-245.
2. Caginalp G., Fife P.C. Dynamics of layered interfaces arising from phase boundaries. SIAM J. Appl. Math. 48(3):1988;506-518.
3. P.C. Fife, Dynamics of Internal Layers and Diffusive Interfaces, Regional Conference Series in Applied Mathematics, Vol. 53, 1988.
4. Jäckle J. Models of the glass transition. Rep. Prog. Phys. 49:1986;171-231.
5. Jäckle J. Heat conduction and relaxation in liquids of high viscosity. Physica A. 162:1990;377-404.
6. Binder K., Frisch H.L., Jäckle J. Kinetics of phase separation in the presence of slowly relaxing structural variables. J. Chem. Phys. 85:1986;1505-1512.
7. Jäckle J., Frisch H.L. Relaxation of chemical potential and a generalized diffusion equation. J. Polym. Sci. Phys. Ed. 23:1985;674-682.
8. Jäckle J., Frisch H.L. Properties of a generalized diffusion equation with a memory. J. Chem. Phys. 85:1986;1621-1627.
9. H.G. Rotstein, S. Brandon, A. Novick-Cohen, A.A. Nepomnyashchy, Hyperbolic phase transition dynamics in two dimensions, submitted for publication.
10. Rotstein H.G., Nepomnyashchy A.A. Dynamics of kinks in two-dimensional hyperbolic models. Physica D. 136:2000;245-265.
11. H.G. Rotstein, Phase transition dynamics with memory, Ph.D. Thesis, Department of Mathematics, Technion, Israel Institute of Technology, Haifa, Israel.
12. Cahn J.W., Hilliard J.E. Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28:1986;258-267.
13. A. Novick-Cohen, On the viscous Cahn-Hilliard equation, in: J.M. Ball (Ed.), Material Instabilities in Continuum Mechanics and Related Problems, Proceedings of the Heriot-Watt Symposium on Nonclassical Continuum Mechanics, 1986, Oxford University Press, Oxford, 1987, pp. 329-342.
14. Aizicovici S., Barbu V. Existence and asymptotic results for a system of integro-partial differential equations. Nonlinear Differ. Equations Appl. 3:1996;1-18.
15. A. Novick-Cohen, Conserved phase-field equations with memory, in: Proceedings of the International Conference on Curvature Flows and Related Topics, Mathematica Sciences and Applications, Vol. 5, 1995, pp. 179-198.
16. Fife P.C., Penrose O. Interfacial dynamics for thermodynamically consistent phase-field models with nonconserved order parameter. Electron. J. Differential Equations. 16:1995;1-49.
17. Neu J.C. Kinks and the minimal surface equation in Minkowski space. Physica D. 43:1990;421-434.
18. Rubinstein J., Sternberg P., Keller J.B. Fast reaction, slow diffusion and curve shortening. SIAM J. Appl. Math. 49(1):1989;116-133.
19. Caginalp G. The dynamics of a conserved phase field system: Stefan-like, Hele-Shaw, and Cahn-Hilliard models as asymptotic limits. IMA J. Appl. Math. 44:1990;77-94.
20. Caginalp G. Phase field models and sharp interface limits: some differences in subtle situations. Rocky Mountain J. Math. 21(2):1991;603-616.
21. H.G. Rotstein, A.I. Domoshnitsky, A.A. Nepomnyashchy, Phase transition dynamics with memory, in: Proceedings of the Israel Seminar, Funct. Differential Equations 9 (1999) 1-12.