Geodesic
Limiting behavior of global attractors for singularly perturbed beam equations with strong damping
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 1, pp. 45-60

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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.
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.
Classification : 35B25, 35B40, 35Q20, 35Q72, 37C70, 47H20, 73K05, 74H45, 74K10
Keywords: strongly damped beam equation; compact attractor; upper semicontinuity of global attractors 
Ševčovič, Daniel. Limiting behavior of global attractors  for singularly perturbed beam equations  with strong damping. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 1, pp. 45-60. http://geodesic.mathdoc.fr/item/CMUC_1991_32_1_a6/
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     title = {Limiting behavior of global attractors  for singularly perturbed beam equations  with strong damping},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {45--60},
     year = {1991},
     volume = {32},
     number = {1},
     mrnumber = {1118289},
     zbl = {0741.35089},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1991_32_1_a6/}
}
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