A modified Swift-Hohenberg equation

Abstract

We consider the initial-boundary value problem for a modified Swift-Hohenberg equation in space dimension $n\leq 7 $. Based on the semigroup theory, we formulate this problem as an abstract evolutionary equation with sectorial operator in the main part. We show that the semigroup generated by this problem admits a global attractor in the phase space $H^2(\Omega)\cap H^{1}_{0}(\Omega)$ and characterize the contents of the attractor.