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Discrete and Continuous Dynamical Systems - Series S (DCDS-S)
 

Asymptotic behavior of the Caginalp phase-field system with coupled dynamic boundary conditions
Pages: 485 - 505, Issue 3, June 2012

doi:10.3934/dcdss.2012.5.485      Abstract        References        Full text (430.3K)           Related Articles

Monica Conti - Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano, Italy (email)
Stefania Gatti - Dipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi 213/B, I-41125 Modena, Italy (email)
Alain Miranville - Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 6086 - SP2MI, Boulevard Marie et Pierre Curie - Téléport 2, F-86962 Chasseneuil Futuroscope Cedex, France (email)

1 G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Rational Mech. Anal., 92 (1986), 205-245.       
2 P. Fabrie, C. Galusinski, A. Miranville and S. Zelik, Uniform exponential attractors for a singularly perturbed damped wave equation. Partial differential equations and applications, Discrete Contin. Dynam. Systems, 10 (2004), 211-238.       
3 H. P. Fischer, P. Maass and W. Dieterich, Novel surface modes in spinodal decomposition, Phys. Rev. Letters, 79 (1997), 893-896.
4 H. P. Fischer, P. Maass and W. Dieterich, Diverging time and length scales of spinodal decomposition modes in thin flows, Europhys. Lett., 42 (1998), 49-54.
5 H. P. Fischer, J. Reinhard, W. Dieterich, J.-F. Gouyet, P. Maass, A. Majhofer and D. Reinel, Time-dependent density functional theory and the kinetics of lattice gas systems in contact with a wall, J. Chem. Phys., 108 (1998), 3028-3037.
6 C. G. Gal, M. Grasselli and A. Miranville, Robust exponential attractors for singularly perturbed phase-field equations with dynamic boundary conditions, NoDEA Nonlinear Differential Equations Appl., 15 (2008), 535–-556.       
7 C. G. Gal, M. Grasselli and A. Miranville, Nonisothermal Allen-Cahn equations with coupled dynamic boundary conditions, in "Nonlinear Phenomena with Energy Dissipation," GAKUTO Internat. Ser. Math. Sci. Appl., 29, Gakkotōsho, Tokyo, 2008, 117–-139.       
8 S. Gatti and A. Miranville, Asymptotic behavior of a phase-field system with dynamic boundary conditions, in "Differential Equations: Inverse and Direct Problems," Lecture Notes in Pure and Applied Mathematics, 251, Chapman & Hall/CRC, Boca Raton, FL, (2006), 149-170.       
9 M. Grasselli, A. Miranville and G. Schimperna, The Caginalp phase-field system with coupled dynamic boundary conditions and singular potentials, Discrete Contin. Dynam. Systems, 28 (2010), 67-98.       
10 O. A. Ladyžhenskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Translations of Mathematical Monographs, Vol. 23, AMS, Providence, RI, 1967.       
11 A. Miranville and S. Zelik, Robust exponential attractors for singularly perturbed phase-field type equations, Electron. J. Differential Equations, 2002, 28 pp.       
12 A. Miranville and S. Zelik, Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions, Math. Meth. Appl. Sci., 28 (2005), 709-735.       
13 A. Miranville and S. Zelik, The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions, Discrete Contin. Dynam. Systems, 28 (2010), 275-310.       
14 R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics," 2nd edition, Applied Mathematical Sciences, 68, Springer-Verlag, New York, 1997.       
15 E. Zeidler, "Nonlinear Functional Analysis and its Applications. Part I. Fixed-Point Theorems," Springer-Verlag, New York, 1986.       

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