Regularity of Global Attractor for the Reaction-Diffusion Equation

Abstract

By using an iteration procedure, regularity estimates for the linear semigroups, and a classical existence theorem of global attractor, we prove that the reaction-diffusion equation possesses a global attractor in Sobolev space $H^k$ for all $k>0$, which attracts any bounded subset of $H^k$($\Omega$) in the $H^k$-norm.