Singular dynamics of strongly damped beam equation

The paper is devoted to the dynamics of the model for a beam with strong damping where is continuously differentiable, and α,l,ε>0, subject to boundary conditions corresponding to hinged or clamped ends. We show that for ε→0+ the dynamics of the equation is close to the dynamics of equation where Au:=uxxxx with the domain determined by one of the above boundary conditions. Specifically, we show that isolated invariant sets of (P0) continue to isolated invariant sets of (Pε), ε>0 small, having the same Conley index. Moreover, isolated Morse decompositions with respect to (P0) continue to isolated Morse decompositions of (Pε), ε>0 small, having isomorphic homology index braids. Under some additional assumptions we establish existence and upper semicontinuity results for attractors of (P0) and (Pε), ε>0 small, extending previous results by Ševčovič.