Weak solutions to a phase-field model with non-constant thermal conductivity

Quarterly of Applied Mathematics

Volumn 55, Issue 4, 1997, Pages 739-760

  Laurencot P H ^a  

^a UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FREE ENERGY; MATHEMATICAL MODELS; SET THEORY; THERMAL CONDUCTIVITY OF LIQUIDS;

CAHN HILLIARD EQUATION; PHASE FIELD MODEL;

PHASE TRANSITIONS;

MODEL; THERMAL CONDUCTIVITY;

EID: 0031402415     PISSN: 0033569X     EISSN: None     Source Type: Journal    
DOI: 10.1090/qam/1486546     Document Type: Article

References (17)

1. J. F. Blowey and C. M. Elliott, A phase-field model with a double obstacle potential, in Motion by Mean Curvature and Related Topics, G. Buttazzo, A. Visintin, eds., de Gruyter, Berlin, 1994, pp. 1-22
2. H. Brezis, Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, North Holland, Amsterdam, 1973
3. D. Brochet, X. Chen, and D. Hilhorst, Finite dimensional exponential attractor for the phase field model, Applicable Anal. 49, 197-212 (1993)
4. G. Caginalp, An analysis of a phase field model for a free boundary, Arch. Rational Mech. Anal. 92, 205-245 (1986)
5. G. Caginalp, Stefan and Hele-Shaw type models as asymptotic limits of the phase field equations, Phys. Rev. A 39, 5887-5896 (1989)
6. J. W. Cahn and J. E. Taylor, Surface motion by surface diffusion, Acta Metall. Mater. 42, 1045-1063 (1994)
7. C. M. Elliott and H. Garcke, On the Cahn-Hilliard equation with degenerate mobility, SIAM J. Math. Anal. 27, 404-423 (1996)
8. C. M. Elliott and S. Zheng, Global existence and stability of solutions to the phase field equations, in Free Boundary Value Problems, K. H. Hoffmann, J. Sprekels, eds., Internat. Ser. Num. Math. 95, Birkhäuser, Basel, 1990, pp. 46-58
9. O. Kavian, Introduction à la théorie des points critiques, Mathématiques et Applications 13, SMAI, Springer-Verlag, Paris, 1993
10. N. Kenmochi and M. Niezgódka, Evolution systems of nonlinear variational inequalities arising from phase change problems, Nonlinear Anal., TMA 22, 1163-1180 (1994)
11. M. Langlais and D. Phillips, Stabilization of solutions of nonlinear and degenerate evolution equations, Nonlinear Anal., TMA 9, 321-333 (1985)
12. Ph. Laurençot, Long-time behaviour for a model of phase-field type, Proc. Roy. Soc. Edinburgh 126A, 167-185 (1996)
13. Ph. Laurençot, Degenerate Cahn-Hilliard equation as limit of the phase-field equations with non-constant thermal conductivity, preprint Institut Elie Cartan, Nancy
14. J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Paris, 1969
15. U. Mosco, Convergence of convex sets and of solutions of variational inequalities, Adv. Math. 3, 510-585 (1969)
16. P(0, T; B), Ann. Mat. Pura Appl. 146, 65-96 (1987)
17. B. E. E. Stoth, The Cahn-Hilliard equation as degenerate limit of the phase-field equations, Quart. Appl. Math. 53, 695-700 (1995)