Long time behavior of the Caginalp system with singular potentials and dynamic boundary conditions
Laurence Cherfils - Université de La Rochelle, Laboratoire de Mathématiques Images et Applications EA 3165, Avenue Michel Crépeau, 17042 La Rochelle Cedex 1, 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
Received: December 2010; Revised: December 2010; Published: April 2012.
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