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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, Volume 5, Issue 3, June 2012      doi:10.3934/dcdss.2012.5.485

 
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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)

Abstract: 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.

Keywords:  Caginalp system, phase transition, dynamic boundary conditions, global attractor, exponential attractor.
Mathematics Subject Classification:  Primary: 35K55, 35J60; Secondary: 80A22.

Received: May 2011;      Revised: July 2011;      Available Online: October 2011.

 References