American Institute of Mathematical Sciences

June  2012, 5(3): 485-505. doi: 10.3934/dcdss.2012.5.485

Asymptotic behavior of the Caginalp phase-field system with coupled dynamic boundary conditions

 1 Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano 2 Dipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi 213/B, I-41125 Modena, Italy 3 Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 6086 - SP2MI, Boulevard Marie et Pierre Curie - Téléport 2, F-86962 Chasseneuil Futuroscope Cedex

Received  May 2011 Revised  July 2011 Published  October 2011

This paper deals with the longtime behavior of the Caginalp phase-field system with coupled dynamic boundary conditions on both state variables. We prove that the system generates a dissipative semigroup in a suitable phase-space and possesses the finite-dimensional smooth global attractor and an exponential attractor.
Citation: Monica Conti, Stefania Gatti, Alain Miranville. Asymptotic behavior of the Caginalp phase-field system with coupled dynamic boundary conditions. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 485-505. doi: 10.3934/dcdss.2012.5.485
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