A class of time discrete schemes for a phase-field system of Penrose-Fife type
ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 6, pp. 1261-1292.
@article{M2AN_1999__33_6_1261_0,
     author = {Klein, Olaf},
     title = {A class of time discrete schemes for a phase-field system of {Penrose-Fife} type},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {1261--1292},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {6},
     year = {1999},
     mrnumber = {1736899},
     zbl = {0951.65085},
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     url = {http://www.numdam.org/item/M2AN_1999__33_6_1261_0/}
}
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Klein, Olaf. A class of time discrete schemes for a phase-field system of Penrose-Fife type. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 6, pp. 1261-1292. http://www.numdam.org/item/M2AN_1999__33_6_1261_0/

[1] H. Amann, Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems, in Function Spaces, Differential Operators and Nonlinear Analysis, H.-J. Schmeisser and H. Triebel Eds, B. G. Teubner (1993). | MR | Zbl

[2] V. Barbu, Nonlinear semigroups and differential equations in Banach spaces. Noordhoff International Publishing (1976). | MR | Zbl

[3] 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 and A. Visintin Eds., De Gruyter, New York (1994) 1-22. | MR | Zbl

[4] H. Brézis, Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, in Contributions to Nonlinear Functional Analysis, E.H. Zarantonello Ed., Academic Press, London (1971) 101-155. | MR | Zbl

[5] P. Colli and Ph. Laurençot, Weak solutions to the Penrose-Fife phase field model for a class of admissible heat flux laws. Physica D 111 (1998) 311-334. | MR | Zbl

[6] P. Colli, P. Laurençot and J. Sprekels, Global solution to the Penrose-Fife phase field model with special heat flux laws, in Variations of domain and free-boundary problems in solid mechanics (Paris, 1997), Kluwer Acad. Publ., Dordrecht (1999) 181-188. | MR

[7] P. Colli, Error estimates for nonlinear Stefan problems obtained as asymptotic limits of a Penrose-Fife model. Z. Angew. Math. Mech. 76 (1996) 409-412. | MR | Zbl

[8] P. Colli and J. Sprekels, Stefan problems and the Penrose-Fife phase field model. Adv. Math. Sci. Appl. 7 (1997) 911-934. | MR | Zbl

[9] P. Colli and J. Sprekels, Weak solution to some Penrose-Fife phase-field systems with temperature-dependent memory. J. Differential Equations 142 (1998) 54-77. | MR | Zbl

[10] A. Damlamian and N. Kenmochi, Evolution equations associated with non-isothermal phase transitions, in Functional analysis and global analysis (Quezon City, 1996), Springer, Singapore (1997) 62-77. | MR | Zbl

[11] R. Glowinski, Numerical Methods for Nonlinear Variational Problems. Springer (1984). | Zbl

[12] W. Horn, Ph. Laurençot and J. Sprekels, Global solutions to a Penrose-Fife phase-field model under flux boundary conditions for the inverse temperature. Math. Methods Appl. Sci. 19 (1996) 1053-1072. | MR | Zbl

[13] W. Horn, A numerical scheme for the one-dimensional Penrose-Fife model for phase transitions. Adv. Math. Sci. Appl. 2 (1993) 457-483. | MR | Zbl

[14] W. Horn and J. Sprekels, A numerical method for a singular system of parabolic equations in two space dimensions (unpublished manuscript).

[15] W. Horn, J. Sprekels and S. Zheng, Global existence of smooth solutions to the Penrose-Fife model for Ising ferromagnets. Adv. Math. Sci. Appl. 6 (1996) 227-241. | MR | Zbl

[16] O. Klein, Existence and approximation results for phase-field systems of Penrose-Fife type and Stefan problems. Ph.D. thesis, Humboldt University, Berlin (1997).

[17] O. Klein, A semidiscrete scheme for a Penrose-Fife system and some Stefan problems in R3. Adv. Math. Sci. Appl. 7 (1997) 491-523. | MR | Zbl

[18] N. Kenmochi and M. Kubo, Weak solutions of nonlinear systems for non-isothermal phase transitions. Adv. Math. Sci. Appl. 9 (1999) 499-521. | MR | Zbl

[19] N. Kenmochi and M. Niczgódka, Systems of nonlinear parabolic equations for phase change problems. Adv. Math. Sci. Appl. 3 (1993/94) 89-185. | MR | Zbl

[20] Ph. Laurençot, Étude de quelques problèmes aux dérivées partielles non linéaires. Ph.D. thesis, University of Franche-Comté, France (1993).

[21] Ph. Laurençot, Solutions to a Penrose-Fife model of phase-field type. J. Math. Anal. Appl. 185 (1994) 262-274. | MR | Zbl

[22] Ph. Laurençot, Weak solutions to a Penrose-Fife model for phase transitions. Adv. Math. Sci. Appl. 5 (1995) 117-138. | MR | Zbl

[23] Ph. Laurençot, Weak solutions to a Penrose-Fife model with Fourier law for the temperature. J. Math. Anal. Appl. 219 (1998) 331-343. | MR | Zbl

[24] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod Gauthier-Villars, Paris (1969). | MR | Zbl

[25] M. Marcus and V.J. Mizel, Absolute continuity on tracks and mappings of Sobolev spaces. Arch. Rational Mech. Anal. 45 (1972) 294-320. | MR | Zbl

[26] M. Marcus and V.J. Mizel, Complete characterization of functions which act, via superposition, on Sobolev spaces. Trans. Amer. Math. Soc. 251 (1979) 187-218. | MR | Zbl

[27] M. Niezgódka and J. Sprekels, Convergent numerical approximations of the thermomechanical phase transitions in shape memory alloys. Numer. Math. 58 (1991) 759-778. | MR | Zbl

[28] R.H. Nochetto, G. Savaré and C. Verdi, A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations. Comm. Pure Appl. Math. (to appear). | MR | Zbl

[29] 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. | MR | Zbl

[30] J. Sprekels and 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. | MR | Zbl

[31] E. Zeidler, Nonlinear Functional Analysis and its Applications Il/A: Linear Monotone Operators. Springer (1990). | MR | Zbl

[32] S. Zheng, Nonlinear parabolic equations and hyperbolic-parabolic coupled systems, in Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 76, Longman (1995). | MR | Zbl