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On the hyperbolic relaxation of the one-dimensional Cahn-Hilliard equation |
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| Authors: | Stefania Gatti Vittorino Pata |
| Affiliation: | a Dipartimento di Matematica, Università di Ferrara, via Machiavelli 35, I-44100 Ferrara, Italy b Dipartimento di Matematica “F. Brioschi,” Politecnico di Milano, via Bonardi 9, I-20133 Milano, Italy c Université de Poitiers, Laboratoire d'Applications des Mathématiques, SP2MI, Boulevard Marie et Pierre Curie, Téléport 2, F-86962 Chasseneuil Futuroscope cedex, France |
| Abstract: | We consider the one-dimensional Cahn-Hilliard equation with an inertial term ?utt, for ??0. This equation, endowed with proper boundary conditions, generates a strongly continuous semigroup S?(t) which acts on a suitable phase-space and possesses a global attractor. Our main result is the construction of a robust family of exponential attractors {M?}, whose common basins of attraction are the whole phase-space. |
| Keywords: | Cahn-Hilliard equation Strongly continuous semigroups Absorbing sets Global attractors Robust exponential attractors |
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