[1] H. W. Alt, I. Pawlow:
A mathematical model of dynamics of non-isothermal phase separation. Physica D 59 (1992), 389–416.
MR 1192751
[2] V. Barbu:
Nonlinear Semigroups and Differential Equations in Banach Spaces. Noordhoff, Leyden, 1976.
MR 0390843 |
Zbl 0328.47035
[3] H. Brezis:
Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Math. Stud. Vol. 5 North-Holland, Amsterdam, 1973.
MR 0348562 |
Zbl 0252.47055
[5] J. W. Cahn, J. Hilliard:
Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28 (1958), 258–267.
DOI 10.1063/1.1744102
[6] P. Colli, G. Gilardi, M. Grasselli, and G. Schimperna:
The conserved phase-field system with memory. Adv. Math. Sci. Appl. 11 (2001), 265–291.
MR 1841569
[7] P. Colli, G. Gilardi, E. Rocca, and G. Schimperna:
On a Penrose-Fife phase field model with inhomogeneous Neumann boundary conditions for the temperature. Differ. Integral Equ. 17 (2004), 511–534.
MR 2054932
[8] P. Colli, Ph. Laurençot:
Weak solutions to the Penrose-Fife phase field model for a class of admissible flux laws. Physica D 111 (1998), 311–334.
MR 1601442
[9] P. Colli, Ph. Laurençot, and J. Sprekels:
Global solution to the Penrose-Fife phase field model with special heat flux laws. In: Variations of Domains and Free-Boundary Problems in Solid Mechanics. Solid Mech. Appl. 66, P. Argoul, M. Frémond, Q. S. Nguyen (eds.), Kluwer Acad. Publ., Dordrecht, 1999, pp. 181–188.
MR 1672241
[10] P. Colli, J. Sprekels:
On a Penrose-Fife model with zero interfacial energy leading to a phase-field system of relaxed Stefan type. Ann. Mat. Pura Appl. IV. Ser. 169 (1995), 269–289.
DOI 10.1007/BF01759357 |
MR 1378478
[11] G. Gilardi, A. Marson:
On a Penrose-Fife type system with Dirichlet boundary conditions for the temperature. Math. Methods Appl. Sci. 26 (2003), 1303–1325.
DOI 10.1002/mma.423 |
MR 2004103
[13] W. Horn, J. Sprekels, and S. Zheng:
Global existence of smooth solution to the Penrose-Fife model for Ising ferromagnets. Adv. Math. Sci. Appl. 6 (1996), 227–241.
MR 1385769
[14] A. Ito, N. Kenmochi, and M. Kubo:
Non-isothermal phase transition models with Neumann boundary conditions. Nonlinear Anal. Theory Methods Appl. 53A (2003), 977-996.
MR 1978030
[15] N. Kenmochi:
Uniqueness of the solution to a nonlinear system arising in phase transition. Proceedings of the Conference Nonlinear Analysis and Applications (Warsaw, 1994). GAKUTO Intern. Ser. Math. Sci. Apl. Vol. 7, N. Kenmochi (ed.), 1995, pp. 261–271.
MR 1422940 |
Zbl 0873.35040
[16] N. Kenmochi, M. Kubo:
Weak solutions of nonlinear systems for non-isothermal phase transitions. Adv. Math. Sci. Appl. 9 (1999), 499–521.
MR 1690439
[17] N. Kenmochi, M. Niezgódka:
Evolution equations of nonlinear variational inequalities arising from phase change problems. Nonlinear Anal. Theory Methods Appl. 22 (1994), 1163–1180.
MR 1279139
[18] N. Kenmochi, M. Niezgódka:
Viscosity approach to modelling non-isothermal diffusive phase separation. Japan J. Ind. Appl. Math. 13 (1996), 135–169.
DOI 10.1007/BF03167303 |
MR 1377464
[20] Ph. Laurençot:
Weak solutions to a Penrose-Fife model for phase transitions. Adv. Math. Sci. Appl. 5 (1995), 117–138.
MR 1325962
[22] J.-L. Lions:
Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Gauthier-Villars, Paris, 1969.
MR 0259693 |
Zbl 0189.40603
[23] J. Nečas:
Les méthodes directes en théorie des équations elliptiques. Masson, Paris, 1967.
MR 0227584
[24] O. Penrose:
Statistical Mechanics and the kinetics of phase separation. In: Material Instabilities in Continuum Mechanics, J. Ball (ed.), Oxford University Press, Oxford, 1988, pp. 373–394.
MR 0970534
[26] O. Penrose, P. C. Fife:
On the relation between the standard phase-field model and a “thermodynamically consistent” phase-field model. Physica D 69 (1993), 107–113.
DOI 10.1016/0167-2789(93)90183-2 |
MR 1245658
[28] E. Rocca, G. Schimperna:
The conserved Penrose-Fife system with Fourier heat flux law. Nonlinear Anal. Theory Methods Appl. 53A (2003), 1089–1100.
MR 1978036
[30] J. Sprekels, S. Zheng:
Global smooth solutions to a thermodynamically consistent model of phase-field type in higher space dimensions. J. Math. Anal. Appl. 176 (1993), 200–223.
DOI 10.1006/jmaa.1993.1209 |
MR 1222165
[31] H. E. Stanley: Introduction to Phase Transitions and Critical Phenomena. Oxford University Press, Oxford, 1987.