Exponential Attractor for the Boussinesq Equation with Strong Damping and Clamped Boundary Condition
The paper studies the existence of exponential attractor for the Boussinesq equation with strong damping and clamped boundary condition utt-Δu+Δ2u-Δut-Δg(u)=f(x). The main result is concerned with nonlinearities g(u) with supercritical growth. In that case, we construct a bounded absorbing set with...
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2016-01-01
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Series: | Discrete Dynamics in Nature and Society |
Online Access: | http://dx.doi.org/10.1155/2016/5036048 |
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doaj-e2b131a982de4b859a0c723a1c93c1bd2020-11-24T23:47:24ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/50360485036048Exponential Attractor for the Boussinesq Equation with Strong Damping and Clamped Boundary ConditionFan Geng0Ruizhai Li1Xiaojun Zhang2Xiangyu Ge3School of Arts and Science, Sias International University, Zhengzhou 451150, ChinaSchool of Arts and Science, Sias International University, Zhengzhou 451150, ChinaWuhan Technology and Business University, Wuhan 430065, ChinaWuhan Technology and Business University, Wuhan 430065, ChinaThe paper studies the existence of exponential attractor for the Boussinesq equation with strong damping and clamped boundary condition utt-Δu+Δ2u-Δut-Δg(u)=f(x). The main result is concerned with nonlinearities g(u) with supercritical growth. In that case, we construct a bounded absorbing set with further regularity and obtain quasi-stability estimates. Then the exponential attractor is established in natural energy space V2×H.http://dx.doi.org/10.1155/2016/5036048 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Fan Geng Ruizhai Li Xiaojun Zhang Xiangyu Ge |
spellingShingle |
Fan Geng Ruizhai Li Xiaojun Zhang Xiangyu Ge Exponential Attractor for the Boussinesq Equation with Strong Damping and Clamped Boundary Condition Discrete Dynamics in Nature and Society |
author_facet |
Fan Geng Ruizhai Li Xiaojun Zhang Xiangyu Ge |
author_sort |
Fan Geng |
title |
Exponential Attractor for the Boussinesq Equation with Strong Damping and Clamped Boundary Condition |
title_short |
Exponential Attractor for the Boussinesq Equation with Strong Damping and Clamped Boundary Condition |
title_full |
Exponential Attractor for the Boussinesq Equation with Strong Damping and Clamped Boundary Condition |
title_fullStr |
Exponential Attractor for the Boussinesq Equation with Strong Damping and Clamped Boundary Condition |
title_full_unstemmed |
Exponential Attractor for the Boussinesq Equation with Strong Damping and Clamped Boundary Condition |
title_sort |
exponential attractor for the boussinesq equation with strong damping and clamped boundary condition |
publisher |
Hindawi Limited |
series |
Discrete Dynamics in Nature and Society |
issn |
1026-0226 1607-887X |
publishDate |
2016-01-01 |
description |
The paper studies the existence of exponential attractor for the Boussinesq equation with strong damping and clamped boundary condition utt-Δu+Δ2u-Δut-Δg(u)=f(x). The main result is concerned with nonlinearities g(u) with supercritical growth. In that case, we construct a bounded absorbing set with further regularity and obtain quasi-stability estimates. Then the exponential attractor is established in natural energy space V2×H. |
url |
http://dx.doi.org/10.1155/2016/5036048 |
work_keys_str_mv |
AT fangeng exponentialattractorfortheboussinesqequationwithstrongdampingandclampedboundarycondition AT ruizhaili exponentialattractorfortheboussinesqequationwithstrongdampingandclampedboundarycondition AT xiaojunzhang exponentialattractorfortheboussinesqequationwithstrongdampingandclampedboundarycondition AT xiangyuge exponentialattractorfortheboussinesqequationwithstrongdampingandclampedboundarycondition |
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1725489917596794880 |