A class of time discrete schemes for a phase-field system of Penrose-Fife type
- Volume: 33, Issue: 6, page 1261-1292
- ISSN: 0764-583X
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topKlein, Olaf. "A class of time discrete schemes for a phase-field system of Penrose-Fife type." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.6 (1999): 1261-1292. <http://eudml.org/doc/193971>.
@article{Klein1999,
author = {Klein, Olaf},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {time-discrete schemes; initial-boundary value problem; phase-field system},
language = {eng},
number = {6},
pages = {1261-1292},
publisher = {Dunod},
title = {A class of time discrete schemes for a phase-field system of Penrose-Fife type},
url = {http://eudml.org/doc/193971},
volume = {33},
year = {1999},
}
TY - JOUR
AU - Klein, Olaf
TI - A class of time discrete schemes for a phase-field system of Penrose-Fife type
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 6
SP - 1261
EP - 1292
LA - eng
KW - time-discrete schemes; initial-boundary value problem; phase-field system
UR - http://eudml.org/doc/193971
ER -
References
top- [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). Zbl0810.35037MR1242579
- [2] V. Barbu, Nonlinear semigroups and differential equations in Banach spaces. Noordhoff International Publishing (1976). Zbl0328.47035MR390843
- [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. Zbl0809.35168MR1277388
- [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. Zbl0278.47033MR394323
- [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. Zbl0929.35062MR1601442
- [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. MR1672241
- [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. Zbl0890.35162MR1372256
- [8] P. Colli and J. Sprekels, Stefan problems and the Penrose-Fife phase field model. Adv. Math. Sci. Appl. 7 (1997) 911-934. Zbl0892.35158MR1476282
- [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. Zbl0897.45012MR1492877
- [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. Zbl0912.35085MR1658041
- [11] R. Glowinski, Numerical Methods for Nonlinear Variational Problems. Springer (1984). Zbl0536.65054
- [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. Zbl0859.35049MR1402815
- [13] W. Horn, A numerical scheme for the one-dimensional Penrose-Fife model for phase transitions. Adv. Math. Sci. Appl. 2 (1993) 457-483. Zbl0824.65138MR1239269
- [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. Zbl0858.35053MR1385769
- [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. Zbl0883.65103MR1454679
- [18] N. Kenmochi and M. Kubo, Weak solutions of nonlinear systems for non-isothermal phase transitions. Adv. Math. Sci. Appl. 9 (1999) 499-521. Zbl0930.35037MR1690439
- [19] N. Kenmochi and M. Niczgódka, Systems of nonlinear parabolic equations for phase change problems. Adv. Math. Sci. Appl. 3 (1993/94) 89-185. Zbl0827.35015MR1287926
- [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. Zbl0819.35159MR1283056
- [22] Ph. Laurençot, Weak solutions to a Penrose-Fife model for phase transitions. Adv. Math. Sci. Appl. 5 (1995) 117-138. Zbl0829.35148MR1325962
- [23] Ph. Laurençot, Weak solutions to a Penrose-Fife model with Fourier law for the temperature. J. Math. Anal. Appl. 219 (1998) 331-343. Zbl0919.35137MR1606330
- [24] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod Gauthier-Villars, Paris (1969). Zbl0189.40603MR259693
- [25] M. Marcus and V.J. Mizel, Absolute continuity on tracks and mappings of Sobolev spaces. Arch. Rational Mech. Anal. 45 (1972) 294-320. Zbl0236.46033MR338765
- [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. Zbl0417.46035MR531975
- [27] M. Niezgódka and J. Sprekels, Convergent numerical approximations of the thermomechanical phase transitions in shape memory alloys. Numer. Math. 58 (1991) 759-778. Zbl0715.65099MR1090259
- [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). Zbl1021.65047MR1737503
- [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. Zbl0709.76001MR1060043
- [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. Zbl0804.35063MR1222165
- [31] E. Zeidler, Nonlinear Functional Analysis and its Applications Il/A: Linear Monotone Operators. Springer (1990). Zbl0684.47029MR1033497
- [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). Zbl0835.35003MR1375458
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