A modified Swift-Hohenberg equation

Maria B. Kania

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.

Keywords


Swift-Hohenberg equation; global attractor

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