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Finite dimensional exponential attractor for the phase field model |
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| Authors: | D. Brochet D. Hilhorst Xinfu chen |
| Affiliation: | 1. Laboratoire d'Analyse Numérique , Université Paris Sud , Batiment, Orsay, 425 91405, France;2. Department of Mathematics &3. Statistics , University of Pittsburgh , Pittsburgh, Pennsylvania, 15260, USA |
| Abstract: | We consider the phase field equations in arbitrary space dimension. We show that the corresponding boundary value problems are well-posed when assuming that the initial data is square integrable and prove the existence of a maximal attractor and of an inertial set. |
| Keywords: | Phase field parabolic system semigroup inertial set maximal attractor |