Long time behavior of the Caginalp system with singular potentials and dynamic boundary conditions

Pages: 2261 - 2290, Volume 11, Issue 6, November 2012

doi:10.3934/cpaa.2012.11.2261       Abstract        References        Full Text (1452.0K)       Related Articles

Laurence Cherfils - Université de La Rochelle, Laboratoire de Mathématiques Images et Applications EA 3165, Avenue Michel Crépeau, 17042 La Rochelle Cedex 1, France (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, Mathématiques SP2MI, 86962 Chasseneuil Futuroscope Cedex, France (email)

Abstract: This paper is devoted to the study of the well-posedness and the long time behavior of the Caginalp phase-field model with singular potentials and dynamic boundary conditions. Thanks to a suitable definition of solutions, coinciding with the strong ones under proper assumptions on the bulk and surface potentials, we are able to get dissipative estimates, leading to the existence of the global attractor with finite fractal dimension, as well as of an exponential attractor.

Keywords:  Caginalp model, dynamic boundary conditions, singular potential, variational solutions, global attractor, exponential attractor
Mathematics Subject Classification:  Primary: 35K55, 35J60; Secondary: 80A22

Received: December 2010;      Revised: December 2010;      Published: April 2012.

 References