@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},
year = {1999},
publisher = {EDP Sciences},
volume = {33},
number = {6},
mrnumber = {1736899},
zbl = {0951.65085},
language = {en},
url = {https://www.numdam.org/item/M2AN_1999__33_6_1261_0/}
}
TY - JOUR AU - Klein, Olaf TI - A class of time discrete schemes for a phase-field system of Penrose-Fife type JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1999 SP - 1261 EP - 1292 VL - 33 IS - 6 PB - EDP Sciences UR - https://www.numdam.org/item/M2AN_1999__33_6_1261_0/ LA - en ID - M2AN_1999__33_6_1261_0 ER -
%0 Journal Article %A Klein, Olaf %T A class of time discrete schemes for a phase-field system of Penrose-Fife type %J ESAIM: Modélisation mathématique et analyse numérique %D 1999 %P 1261-1292 %V 33 %N 6 %I EDP Sciences %U https://www.numdam.org/item/M2AN_1999__33_6_1261_0/ %G en %F M2AN_1999__33_6_1261_0
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. https://www.numdam.org/item/M2AN_1999__33_6_1261_0/
[1] , 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). | Zbl | MR
[2] , Nonlinear semigroups and differential equations in Banach spaces. Noordhoff International Publishing (1976). | Zbl | MR
[3] and , 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. | Zbl | MR
[4] , 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. | Zbl | MR
[5] and , Weak solutions to the Penrose-Fife phase field model for a class of admissible heat flux laws. Physica D 111 (1998) 311-334. | Zbl | MR
[6] , and , 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] , Error estimates for nonlinear Stefan problems obtained as asymptotic limits of a Penrose-Fife model. Z. Angew. Math. Mech. 76 (1996) 409-412. | Zbl | MR
[8] and , Stefan problems and the Penrose-Fife phase field model. Adv. Math. Sci. Appl. 7 (1997) 911-934. | Zbl | MR
[9] and , Weak solution to some Penrose-Fife phase-field systems with temperature-dependent memory. J. Differential Equations 142 (1998) 54-77. | Zbl | MR
[10] and , Evolution equations associated with non-isothermal phase transitions, in Functional analysis and global analysis (Quezon City, 1996), Springer, Singapore (1997) 62-77. | Zbl | MR
[11] , Numerical Methods for Nonlinear Variational Problems. Springer (1984). | Zbl
[12] , and , 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. | Zbl | MR
[13] , A numerical scheme for the one-dimensional Penrose-Fife model for phase transitions. Adv. Math. Sci. Appl. 2 (1993) 457-483. | Zbl | MR
[14] and , A numerical method for a singular system of parabolic equations in two space dimensions (unpublished manuscript).
[15] , and , Global existence of smooth solutions to the Penrose-Fife model for Ising ferromagnets. Adv. Math. Sci. Appl. 6 (1996) 227-241. | Zbl | MR
[16] , Existence and approximation results for phase-field systems of Penrose-Fife type and Stefan problems. Ph.D. thesis, Humboldt University, Berlin (1997).
[17] , A semidiscrete scheme for a Penrose-Fife system and some Stefan problems in R3. Adv. Math. Sci. Appl. 7 (1997) 491-523. | Zbl | MR
[18] and , Weak solutions of nonlinear systems for non-isothermal phase transitions. Adv. Math. Sci. Appl. 9 (1999) 499-521. | Zbl | MR
[19] and , Systems of nonlinear parabolic equations for phase change problems. Adv. Math. Sci. Appl. 3 (1993/94) 89-185. | Zbl | MR
[20] , Étude de quelques problèmes aux dérivées partielles non linéaires. Ph.D. thesis, University of Franche-Comté, France (1993).
[21] , Solutions to a Penrose-Fife model of phase-field type. J. Math. Anal. Appl. 185 (1994) 262-274. | Zbl | MR
[22] , Weak solutions to a Penrose-Fife model for phase transitions. Adv. Math. Sci. Appl. 5 (1995) 117-138. | Zbl | MR
[23] , Weak solutions to a Penrose-Fife model with Fourier law for the temperature. J. Math. Anal. Appl. 219 (1998) 331-343. | Zbl | MR
[24] , Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod Gauthier-Villars, Paris (1969). | Zbl | MR
[25] and , Absolute continuity on tracks and mappings of Sobolev spaces. Arch. Rational Mech. Anal. 45 (1972) 294-320. | Zbl | MR
[26] and , Complete characterization of functions which act, via superposition, on Sobolev spaces. Trans. Amer. Math. Soc. 251 (1979) 187-218. | Zbl | MR
[27] and , Convergent numerical approximations of the thermomechanical phase transitions in shape memory alloys. Numer. Math. 58 (1991) 759-778. | Zbl | MR
[28] , and , A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations. Comm. Pure Appl. Math. (to appear). | Zbl | MR
[29] and , Thermodynamically consistent models of phase-field type for the kinetics of phase transitions. Physica D 43 (1990) 44-62. | Zbl | MR
[30] and , Global smooth solutions to a thermodynamically consistent model of phase-field type in higher space dimensions. J. Math. Anal. Appl. 176 (1993) 200-223. | Zbl | MR
[31] , Nonlinear Functional Analysis and its Applications Il/A: Linear Monotone Operators. Springer (1990). | Zbl | MR
[32] , Nonlinear parabolic equations and hyperbolic-parabolic coupled systems, in Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 76, Longman (1995). | Zbl | MR





