Exponential Attractor for the Boussinesq Equation with Strong Damping and Clamped Boundary Condition

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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Main Authors: Fan Geng, Ruizhai Li, Xiaojun Zhang, Xiangyu Ge
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2016/5036048
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spelling 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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