Global attractor for the perturbed viscous Cahn–Hilliard equation
Volume 109 / 2007
Colloquium Mathematicum 109 (2007), 217-229
MSC: Primary 35L70; Secondary 35B41.
DOI: 10.4064/cm109-2-4
Abstract
We consider the initial-boundary value problem for the perturbed viscous Cahn–Hilliard equation in space dimension $n\leq 3$. Applying semigroup theory, we formulate this problem as an abstract evolutionary equation with a sectorial operator in the main part. We show that the semigroup generated by this problem admits a global attractor in the phase space $(H^2({\mit\Omega} )\cap H^{1}_{0}({\mit\Omega} ))\times L^2({\mit\Omega} )$ and characterize its structure.
