Viscosity approach to modelling non-isothermal diffusive phase separation

Japan Journal of Industrial and Applied Mathematics

Volumn 13, Issue 1, 1996, Pages 135-169

  Kenmochi, Nobuyuki ^a   Niezgódka, Marek ^b  

^a CHIBA UNIVERSITY   (Japan)

^b UNIVERSITY OF WARSAW   (Poland)

Author keywords

Constraints; Non isothermal; Phase separation; Viscosity

Indexed keywords

EID: 0000209407     PISSN: 09167005     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03167303     Document Type: Article

References (23)

1. H.W. Alt and I. Pawlow, Existence of solutions for non-isothermal phase separation. Adv. Math. Sci. Appl., 1 (1992), 319-409.
2. J.F. Blowey and C.M. Elliott, The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy, Part I: Mathematical analysis. European J. Appl. Math., 2 (1991), 233-280.
3. H. Brézis, Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert. North-Holland, Amsterdam, 1973.
4. H. Brézis, M.G. Crandall and A. Pazy, Perturbations of nonlinear maximal monotone sets in Banach space. Comm. Pure Appl. Math., 23 (1970), 123-144.
5. P. Colli and A. Visintin, On a class of doubly nonlinear evolution equations. Comm. Partial Differential Equations, 15 (1990), 737-756.
6. S.R. DeGroot and P. Mazur, Non-Equilibrium Thermodynamics. Dover Publ., New York, 1984.
7. E. DiBenedetto and R.E. Showalter, A pseudo-parabolic variational inequality and Stefan problem. Nonlinear Anal. TMA, 6 (1982),279-291.
8. C.E. Elliott, The Cahn-Hilliard model for the kinetics of phase separation. Mathematical Models for Phase Change Problems (ed. J.F. Rodrigues), ISNM 88, Birkhäuser, Basel, 1989, 35-73.
9. C.M. Elliott and S. Zheng, On the Cahn-Hilliard equation. Arch. Rational Mech. Anal., 96 (1986), 339-357.
10. N. Kenmochi and M. Niezgódka, Large time behaviour of a nonlinear system for phase separation. Progress in Partial Differential Equations: the Metz Surveys 2 (ed. M. Chipot), Pitman Research Notes Math. Ser., 296, Longman, New-York, 1993, 12-22.
11. N. Kenmochi and M. Niezgódka, Nonlinear system for non-isothermal diffusive phase separation. J. Math. Anal. Appl., 188 (1994), 651-679.
12. N. Kenmochi and M. Niezgódka, Systems of nonlinear parabolic equations for phase change problems. Adv. Math. Sci. Appl., 3 (1994), 87-115.
13. N. Kenmochi, M. Niezgódka and I. Pawlow, Subdifferential operator approach to the Cahn-Hilliard equation with constraint. J. Differential Equations, 117 (1995), 320-356.
14. N. Kenmochi and I. Pawlow, A class of nonlinear elliptic-parabolic equations with time-dependent constraints. Nonlinear Anal. TMA, 10 (1986), 1181-1202.
15. J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires. Dunod, Gauthier-Villars, Paris, 1969.
16. J.L. Lions and E. Magenes, Nonhomogeneous Boundary Value Problems and Applications. Vol. 1. Springer-Verlag, New York, 1972-1973.
17. S. Luckhaus and A. Visintin, Phase transition in multicomponent systems. Manuscripta Math., 43 (1983), 261-288.
18. Y. Oono and S. Puri, Study of the phase separation dynamics by use of cell dynamical systems, I. Modelling. Phys. Rev., A 38 (1988), 434-453.
19. O. Penrose and P.C. Fife, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions. Physica D, 43 (1990), 44-62.
20. W. Shen and S. Zheng, On the coupled Cahn-Hilliard equations. Comm. Partial Differential Equations, 18 (1993), 701-727.
21. R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics. Springer Verlag, Berlin, 1988.
22. 2u - Δf(u) = 0. Delft Progr. Rep., 10 (1985), 291-310.
23. S. Zheng, Asymptotic behaviour of the solution to the Cahn-Hilliard equation. Appl. Anal., 23 (1986), 165-184.