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Keywords:
strongly damped beam equation; compact attractor; upper semicontinuity of global attractors
strongly damped beam equation; compact attractor; upper semicontinuity of global attractors
Summary:
The limiting behavior of global attractors $\Cal A_\varepsilon $ for singularly perturbed beam equations $$\varepsilon^2 \frac{\partial^2u}{\partial t^2}+ \varepsilon\delta \frac{\partial u}{\partial t}+A \frac{\partial u}{\partial t}+\alpha Au+g(\|u\|_{1/4}^2)A^{1/2}u=0 $$ 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.
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