Keywords: nonlinear and nonlocal evolution equations; Cahn-Hilliard type dynamics; phase transitions models; existence; uniqueness; long-time behaviour
@article{CMJ_2007_57_4_a1,
author = {Colli, Pierluigi and Krej\v{c}{\'\i}, Pavel and Rocca, Elisabetta and Sprekels, J\"urgen},
title = {Nonlinear evolution inclusions arising from phase change models},
journal = {Czechoslovak Mathematical Journal},
pages = {1067--1098},
year = {2007},
volume = {57},
number = {4},
mrnumber = {2357581},
zbl = {1174.35021},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a1/}
}
TY - JOUR AU - Colli, Pierluigi AU - Krejčí, Pavel AU - Rocca, Elisabetta AU - Sprekels, Jürgen TI - Nonlinear evolution inclusions arising from phase change models JO - Czechoslovak Mathematical Journal PY - 2007 SP - 1067 EP - 1098 VL - 57 IS - 4 UR - http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a1/ LA - en ID - CMJ_2007_57_4_a1 ER -
%0 Journal Article %A Colli, Pierluigi %A Krejčí, Pavel %A Rocca, Elisabetta %A Sprekels, Jürgen %T Nonlinear evolution inclusions arising from phase change models %J Czechoslovak Mathematical Journal %D 2007 %P 1067-1098 %V 57 %N 4 %U http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a1/ %G en %F CMJ_2007_57_4_a1
Colli, Pierluigi; Krejčí, Pavel; Rocca, Elisabetta; Sprekels, Jürgen. Nonlinear evolution inclusions arising from phase change models. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1067-1098. http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a1/
[1] A. Ambrosetti, G. Prodi: A Primer of Nonlinear Analysis. Cambridge Stud. Adv. Math., Vol. 34. Cambridge Univ. Press, Cambridge, 1995. | MR
[2] J.-P. Aubin, I. Ekeland: Applied Nonlinear Analysis. John Wiley & Sons, New York, 1984. | MR
[3] V. Barbu: Nonlinear Semigroups and Differential Equations in Banach Spaces. Noordhoff, Leyden, 1976. | MR | Zbl
[4] P. Bates, J. Han: The Neumann boundary problem for a nonlocal Cahn-Hilliard equation. J. Differ. Equations 212 (2005), 235–277. | DOI | MR
[5] H. Brezis: Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Math. Studies, Vol. 5. North-Holland, Amsterdam, 1973. | MR
[6] M. Brokate, J. Sprekels: Hysteresis and Phase Transitions. Appl. Math. Sci., Vol. 121. Springer-Verlag, New York, 1996. | MR
[7] J. Cahn, J. Hilliard: Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28 (1958), 258–267.
[8] C. K. Chen, P. C. Fife: Nonlocal models of phase transitions in solids. Adv. Math. Sci. Appl. 10 (2000), 821–849. | MR
[9] P. Colli: On some doubly nonlinear evolution equations in Banach spaces. Japan J. Indust. Appl. Math. 9 (1992), 181–203. | DOI | MR | Zbl
[10] P. Colli, A. Visintin: On a class of doubly nonlinear evolution equations. Comm. Partial Differential Equations 15 (1990), 737–756. | DOI | MR
[11] N. Dunford, J.T. Schwartz: Linear Operators. Part I. General Theory. Interscience Publishers, New York, 1958. | MR
[12] T. Fukao, N. Kenmochi, and I. Pawlow: Transmission problems arising in Czochralski process of crystal growth. In: Mathematical Aspects of Modelling Structure Formation Phenomena. GAKUTO Internat. Ser. Math. Sci. Appl., Vol. 17, N. Kenmochi, M. Niezgódka, and M. Ôtani (eds.), Gakkotosho, Tokyo, 2001, pp. 228–243. | MR
[13] H. Gajewski: On a nonlocal model of non-isothermal phase separation. Adv. Math. Sci. Appl. 12 (2002), 569–586. | MR | Zbl
[14] H. Gajewski, K. Zacharias: On a nonlocal phase separation model. J. Math. Anal. Appl. 286 (2003), 11–31. | DOI | MR
[15] G. Giacomin, J. L. Lebowitz: Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits. J. Statist. Phys. 87 (1997), 37–61. | MR
[16] G. Giacomin, J. L. Lebowitz: Phase segregation dynamics in particle systems with long range interactions. II. Interface motion. SIAM J. Appl. Math. 58 (1998), 1707–1729. | DOI | MR
[17] A. Haraux: Systèmes dynamiques dissipatifs et applications. Rech. Math. Appl., Vol. 17. Masson, Paris, 1991. | MR
[18] E. Hille, R. Phillips: Functional Analysis and Semigroups. Amer. Math. Soc. Colloq. Publ., Vol. 31. Am. Math. Soc., Providence, 1957. | MR
[19] N. Kenmochi, M. Niezgódka, and I. Pawlow: Subdifferential operator approach to the Cahn-Hilliard equation with constraint. J. Differ. Equations 117 (1995), 320–356. | DOI | MR
[20] A. Miranville: Generalized Cahn-Hilliard equations based on a microforce balance. J. Appl. Math. 4 (2003), 165–185. | MR | Zbl
[21] J. F. Rodrigues: Variational methods in the Stefan problem. In: Phase Transitions and Hysteresis. Lecture Notes in Math., Vol. 1584, A. Visintin (ed.), Springer-Verlag, Berlin, 1994, pp. 147–212. | MR | Zbl
[22] M. Schechter: Principles of Functional Analysis. Academic Press, New York-London, 1971. | MR | Zbl
[23] J. Simon: Compact sets in the space $L^p(0,T;B)$. Ann. Mat. Pura Appl. 146 (1987), 65–96. | MR
[24] K. Yosida: Functional Analysis. Springer-Verlag, Berlin, 1965. | Zbl