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March  2010, 28(1): 67-98. doi: 10.3934/dcds.2010.28.67

The Caginalp phase-field system with coupled dynamic boundary conditions and singular potentials

Maurizio Grasselli 1, , Alain Miranville 2, and  Giulio Schimperna 3,

1. 

Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi, 9, I-20133 Milano
2. 

Laboratoire de Mathématiques et Applications, UMR CNRS 6086, Université de Poitiers - SP2MI, Boulevard Marie et Pierre Curie, F-86962 Chasseneuil Futuroscope Cedex, France
3. 

Università degli Studi di Pavia, Dipartimento di Matematica "F. Casorati", Via Ferrata 1, 27100 Pavia

Received  August 2009 Revised  January 2010 Published  April 2010

We study in this paper the well-posedness and the asymptotic behavior, in terms of global attractors, of the Caginalp system with coupled dynamic boundary conditions and possibly singular potentials (e.g., of logarithmic type).
Keywords: global attractors., weak solutions, parabolic regularization, Phase-field systems.
Mathematics Subject Classification: Primary: 35B41, 35K60; Secondary: 80A2.
Citation: Maurizio Grasselli, Alain Miranville, Giulio Schimperna. The Caginalp phase-field system with coupled dynamic boundary conditions and singular potentials. Discrete & Continuous Dynamical Systems, 2010, 28 (1) : 67-98. doi: 10.3934/dcds.2010.28.67
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