Exponential attractors for a Cahn-Hilliard model in bounded domains with permeable walls
In a previous article [7], we proposed a model of phase separation in a binary mixture confined to a bounded region which may be contained within porous walls. The boundary conditions were derived from a mass conservation law and variational methods. In the present paper, we study the problem furthe...
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| Format: | Article |
| Language: | English |
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Texas State University
2006-11-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2006/143/abstr.thml |
| Summary: | In a previous article [7], we proposed a model of phase separation in a binary mixture confined to a bounded region which may be contained within porous walls. The boundary conditions were derived from a mass conservation law and variational methods. In the present paper, we study the problem further. Using a Faedo-Galerkin method, we obtain the existence and uniqueness of a global solution to our problem, under more general assumptions than those in [7]. We then study its asymptotic behavior and prove the existence of an exponential attractor (and thus of a global attractor) with finite dimension. |
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| ISSN: | 1072-6691 |