LONG-TIME DYNAMICS OF THE STRONGLY DAMPED SEMILINEAR PLATE EQUATION IN RN

doi:10.1016/S0252-9602(18)30799-9

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (3): 1025-1042.doi: 10.1016/S0252-9602(18)30799-9

LONG-TIME DYNAMICS OF THE STRONGLY DAMPED SEMILINEAR PLATE EQUATION IN R^N

Azer KHANMAMEDOV, Sema YAYLA

Department of Mathematics, Faculty of Science, Hacettepe University, Beytepe 06800, Ankara, Turkey

收稿日期:2017-06-13 出版日期:2018-06-25 发布日期:2018-06-25
通讯作者: Azer KHANMAMEDOV E-mail:azer@hacettepe.edu.tr
作者简介:Sema YAYLA,E-mail:semasimsek@hacettepe.edu.tr
基金资助:
This work was supported by Research Fund of the Hacettepe University. Project Number:FBB-2017-16218.

LONG-TIME DYNAMICS OF THE STRONGLY DAMPED SEMILINEAR PLATE EQUATION IN R^N

Azer KHANMAMEDOV, Sema YAYLA

Department of Mathematics, Faculty of Science, Hacettepe University, Beytepe 06800, Ankara, Turkey

Received:2017-06-13 Online:2018-06-25 Published:2018-06-25
Contact: Azer KHANMAMEDOV E-mail:azer@hacettepe.edu.tr
Supported by:
This work was supported by Research Fund of the Hacettepe University. Project Number:FBB-2017-16218.

摘要/Abstract

摘要：

We investigate the initial-value problem for the semilinear plate equation containing localized strong damping, localized weak damping and nonlocal nonlinearity. We prove that if nonnegative damping coefficients are strictly positive almost everywhere in the exterior of some ball and the sum of these coefficients is positive a.e. in Rⁿ, then the semigroup generated by the considered problem possesses a global attractor in H² (Rⁿ)×L² (Rⁿ). We also establish the boundedness of this attractor in H³ (Rⁿ)×H² (Rⁿ).

关键词: Wave equation, plate equation, global attractor

Abstract:

Key words: Wave equation, plate equation, global attractor

Azer KHANMAMEDOV, Sema YAYLA. LONG-TIME DYNAMICS OF THE STRONGLY DAMPED SEMILINEAR PLATE EQUATION IN R^N[J]. 数学物理学报(英文版), 2018, 38(3): 1025-1042.

Azer KHANMAMEDOV, Sema YAYLA. LONG-TIME DYNAMICS OF THE STRONGLY DAMPED SEMILINEAR PLATE EQUATION IN R^N[J]. Acta mathematica scientia,Series B, 2018, 38(3): 1025-1042.

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LONG-TIME DYNAMICS OF THE STRONGLY DAMPED SEMILINEAR PLATE EQUATION IN R^N

LONG-TIME DYNAMICS OF THE STRONGLY DAMPED SEMILINEAR PLATE EQUATION IN R^N

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