Regularity of global attractor for the reaction-diffusion equation (Q448852)

Summary: 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.