Abstract

In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation u t =Δ u + Λ u − u 3 possesses a global attractor in Sobolev space H k for all k ≥ 0, which attracts any bounded domain of H k (Ω) in the H k -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, ∞).

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call