Daniel \v Sev\v covi\v c
Limiting behavior of global attractors for singularly perturbed beam equations with strong damping

Comment.Math.Univ.Carolinae 32,1 (1991) 45-60.

Abstract:The limiting behavior of global attractors $\Cal A_\varepsilon $ for singularly perturbed beam equations $$ \varepsilon ^2 \frac {\partial ^2 u}{\partial t^2}+ \varepsilon \delta \frac {\partial u}{\partial t}+A \frac {\partial u}{\partial t} + \alpha A u + g(||u||_{1/4}^2) A^{1/2}u=0 $$ is investigated. It is shown that for any neighborhood $\Cal U$ of $\Cal A_0$ the set $\Cal A_\varepsilon $ is included in $\Cal U$ for $\varepsilon $ small.

Keywords: strongly damped beam equation, compact attractor, upper semicontinuity of global attractors
AMS Subject Classification: 35B40, 35Q20