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Finite-dimensional attractor for the viscous Cahn-Hilliard equation in an unbounded domain. (English) Zbl 1115.35025
Summary: We consider the viscous Cahn-Hilliard equation in an infinite domain. Due to the noncompactness of operators, we use weighted Sobolev spaces to prove that the semigroup generated by this equation has the global attractor which has finite Hausdorff dimension.

MSC:
35B41 Attractors
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B40 Asymptotic behavior of solutions to PDEs
35B45 A priori estimates in context of PDEs
35K55 Nonlinear parabolic equations
35K35 Initial-boundary value problems for higher-order parabolic equations
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