| Title:
|
Limiting behavior of global attractors for singularly perturbed beam equations with strong damping (English) |
| Author:
|
Ševčovič, Daniel |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
1 |
| Year:
|
1991 |
| Pages:
|
45-60 |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
strongly damped beam equation |
| Keyword:
|
compact attractor |
| Keyword:
|
upper semicontinuity of global attractors |
| MSC:
|
35B25 |
| MSC:
|
35B40 |
| MSC:
|
35Q20 |
| MSC:
|
35Q72 |
| MSC:
|
37C70 |
| MSC:
|
47H20 |
| MSC:
|
73K05 |
| MSC:
|
74H45 |
| MSC:
|
74K10 |
| idZBL:
|
Zbl 0741.35089 |
| idMR:
|
MR1118289 |
| . |
| Date available:
|
2008-10-09T13:10:59Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116942 |
| . |
| Reference:
|
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| Reference:
|
[B1] Ball J.M.: Initial-boundary value problems for an extensible beam.J. Math. Anal. Appl. 42 (1973), 61-96. Zbl 0254.73042, MR 0319440 |
| Reference:
|
[B2] Ball J.M.: Stability theory for an extensible beam.J. of Diff. Equations 14 (1973), 399-418. Zbl 0247.73054, MR 0331921 |
| Reference:
|
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| Reference:
|
[F] Fitzgibbon W.E.: Strongly damped quasilinear evolution equations.J. of Math. Anal. Appl. 79 (1981), 536-550. Zbl 0476.35040, MR 0606499 |
| Reference:
|
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| Reference:
|
[H] Henry D.: Geometric Theory of Semilinear Parabolic Equations.Lecture Notes in Math. 840, Springer Verlag. Zbl 0663.35001, MR 0610244 |
| Reference:
|
[HR1] Hale J.K., Rougel G.: Upper semicontinuity of an attractor for a singularly perturbed hyperbolic equations.J. of Diff. Equations 73 (1988), 197-215. MR 0943939 |
| Reference:
|
[HR2] Hale J.K., Rougel G.: Lower semicontinuity of an attractor for a singularly perturbed hyperbolic equations.Journal of Dynamics and Diff. Equations 2 (1990), 16-69. MR 1041197 |
| Reference:
|
[M1] Massat P.: Limiting behavior for strongly damped nonlinear wave equations.J. of Diff. Equations 48 (1983), 334-349. MR 0702424 |
| Reference:
|
[M2] Massat P.: Attractivity properties of $\alpha $-contractions.J. of Diff. Equations 48 (1983), 326-333. MR 0702423 |
| . |
