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

Daniel Ševčovič

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 1, page 45-60
  • ISSN: 0010-2628

Abstract

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The limiting behavior of global attractors for singularly perturbed beam equations is investigated. It is shown that for any neighborhood of the set is included in for small.

How to cite

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Ševčovič, Daniel. "Limiting behavior of global attractors for singularly perturbed beam equations with strong damping." Commentationes Mathematicae Universitatis Carolinae 32.1 (1991): 45-60. <http://eudml.org/doc/247247>.

@article{Ševčovič1991,
abstract = {The limiting behavior of global attractors $\mathcal \{A\}_\varepsilon $ for singularly perturbed beam equations \[\varepsilon ^2 \frac\{\partial ^2u\}\{\partial t^2\}+ \varepsilon \delta \frac\{\partial u\}\{\partial t\}+A \frac\{\partial u\}\{\partial t\}+\alpha Au+g(\Vert u\Vert \_\{1/4\}^2)A^\{1/2\}u=0 \] is investigated. It is shown that for any neighborhood $\mathcal \{U\}$ of $\mathcal \{A\}_0$ the set $\mathcal \{A\}_\varepsilon $ is included in $\mathcal \{U\}$ for $\varepsilon $ small.},
author = {Ševčovič, Daniel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {strongly damped beam equation; compact attractor; upper semicontinuity of global attractors; strongly damped beam equation; compact attractor; upper semicontinuity of global attractors},
language = {eng},
number = {1},
pages = {45-60},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Limiting behavior of global attractors for singularly perturbed beam equations with strong damping},
url = {http://eudml.org/doc/247247},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Ševčovič, Daniel
TI - Limiting behavior of global attractors for singularly perturbed beam equations with strong damping
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 1
SP - 45
EP - 60
AB - The limiting behavior of global attractors $\mathcal {A}_\varepsilon $ for singularly perturbed beam equations \[\varepsilon ^2 \frac{\partial ^2u}{\partial t^2}+ \varepsilon \delta \frac{\partial u}{\partial t}+A \frac{\partial u}{\partial t}+\alpha Au+g(\Vert u\Vert _{1/4}^2)A^{1/2}u=0 \] is investigated. It is shown that for any neighborhood $\mathcal {U}$ of $\mathcal {A}_0$ the set $\mathcal {A}_\varepsilon $ is included in $\mathcal {U}$ for $\varepsilon $ small.
LA - eng
KW - strongly damped beam equation; compact attractor; upper semicontinuity of global attractors; strongly damped beam equation; compact attractor; upper semicontinuity of global attractors
UR - http://eudml.org/doc/247247
ER -

References

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