Finite-dimensional attractor for the viscous Cahn-Hilliard equation in an unbounded domain
Ahmed Bonfoh · Quarterly of Applied Mathematics · 2006
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.