Existence of global attractors for a nonlinear evolution equation in Sobolev space Hk

In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation ut =Δu + Λu − u3 possesses a global attractor in Sobolev space Hk for all k ≥ 0, which attracts any bounded domain of Hk(Ω) in the Hk-norm. This result is established by using an iteration technique and regularity estimates for linear semigroup of operator, which extends the classical result from the case k ∈ [0, 1] to the case k ∈ [0, ∞).