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

Maurizio Grasselli; Alain Miranville; Giulio Schimperna

doi:10.3934/dcds.2010.28.67

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2010, Volume 28, Issue 1: 67-98. Doi: 10.3934/dcds.2010.28.67

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

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
3.
Università degli Studi di Pavia, Dipartimento di Matematica "F. Casorati", Via Ferrata 1, 27100 Pavia

Received: July 31, 2009

Revised: December 31, 2009

Published: February 2010

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Abstract

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).

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Mathematics Subject Classification: Primary: 35B41, 35K60; Secondary: 80A22.

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