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

Pages: 67 - 98, Volume 28, Issue 1, September 2010

doi:10.3934/dcds.2010.28.67       Abstract        Full Text (446.8K)       Related Articles

Maurizio Grasselli - Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi, 9, I-20133 Milano, Italy (email)
Alain Miranville - Laboratoire de Mathématiques et Applications, UMR CNRS 6086, Université de Poitiers - SP2MI, Boulevard Marie et Pierre Curie, F-86962 Chasseneuil Futuroscope Cedex, France (email)
Giulio Schimperna - Università degli Studi di Pavia, Dipartimento di Matematica "F. Casorati", Via Ferrata 1, 27100 Pavia, Italy (email)

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).

Keywords:  Phase-field systems, weak solutions, parabolic regularization, global attractors.
Mathematics Subject Classification:  Primary: 35B41, 35K60; Secondary: 80A22.

Received: August 2009;      Revised: January 2010;      Published: April 2010.