Existence of Global Attractor for a Modified Swift - Hohenberg Equation

Abstract

This study mainly aims to explore the existence of global attractor for a modified Swift-Hohenberg equation. The method we use was the classical existence theorem of global attractors and the theory of semigroups. Use this method we prove that the equation exist a global attractor in $H_{\frac{1}{2}}$ space, and the global attractor attracts whatever bounded subset of $H_{\frac{1}{2}}$ in the $H_{\frac{1}{2}}$-norm.