### 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.

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

#### Full Text:

FULL TEXT### Refbacks

- There are currently no refbacks.