### Limiting behavior of global attractors for singularly perturbed beam equations with strong damping

Daniel Ševčovič (1991)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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