Well-posedness and strong attractors for a beam model with degenerated nonlocal strong damping

Abstract

This paper is devoted to initial-boundary value problem of an extensible beam equation with degenerate nonlocal energy damping in Ω ⊂ R n :2 ) q ∆u t + f (u) = 0. We prove the global existence and uniqueness of weak solutions, which gives a positive answer to an open question in [24]. Moreover, we establish the existence of a strong attractor for the corresponding weak solution semigroup, where the "strong" means that the compactness and attractiveness of the attractor are in the topology of a stronger space H1 q .