The existence of global attractor for a Cahn-Hilliard/Allen-Cahn‎ ‎equation

Abstract

In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in $H^k(0<=k<5)$ space of this equation, and it attracts any bounded subset of $H^k(omega)$ in the $H^k$-norm.