Global Attractor of Thermoelastic Coupled Beam Equations with Structural Damping

Global Attractor of Thermoelastic Coupled Beam Equations with Structural Damping

In this paper, we study the existence of a global attractor for a class of n-dimension thermoelastic coupled beam equations with structural damping utt+Δ2u+Δ2ut-[σ(∫Ω‍(∇u)2dx)+ϕ(∫Ω‍∇u∇utdx)]Δu+f1(u)+g(ut)+νΔθ=q(x),  in  Ω×R+, and θt-Δθ+f2(θ)-νΔut=0. Here Ω is a bounded domain of RN, and σ(·) and ϕ(·...

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Main Authors: Peirong Shi, Danxia Wang, Weiyi Chen
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2017/2908964
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spelling doaj-a92f9a9f77b0415192788b09a2a735e62020-11-24T22:56:57ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472017-01-01201710.1155/2017/29089642908964Global Attractor of Thermoelastic Coupled Beam Equations with Structural DampingPeirong Shi0Danxia Wang1Weiyi Chen2Mechanics College, Taiyuan University of Technology, Taiyuan 030024, ChinaDepartment of Mathematics, Taiyuan University of Technology, Taiyuan 030024, ChinaMechanics College, Taiyuan University of Technology, Taiyuan 030024, ChinaIn this paper, we study the existence of a global attractor for a class of n-dimension thermoelastic coupled beam equations with structural damping utt+Δ2u+Δ2ut-[σ(∫Ω‍(∇u)2dx)+ϕ(∫Ω‍∇u∇utdx)]Δu+f1(u)+g(ut)+νΔθ=q(x),  in  Ω×R+, and θt-Δθ+f2(θ)-νΔut=0. Here Ω is a bounded domain of RN, and σ(·) and ϕ(·) are both continuous nonnegative nonlinear real functions and q is a static load. The source terms f1(u) and f2(θ) and nonlinear external damping g(ut) are essentially |u|ρu, |θ|ϱθ, and |ut|rut respectively.http://dx.doi.org/10.1155/2017/2908964
collection DOAJ
language English
format Article
sources DOAJ
author Peirong Shi
Danxia Wang
Weiyi Chen
spellingShingle Peirong Shi
Danxia Wang
Weiyi Chen
Global Attractor of Thermoelastic Coupled Beam Equations with Structural Damping
Mathematical Problems in Engineering
author_facet Peirong Shi
Danxia Wang
Weiyi Chen
author_sort Peirong Shi
title Global Attractor of Thermoelastic Coupled Beam Equations with Structural Damping
title_short Global Attractor of Thermoelastic Coupled Beam Equations with Structural Damping
title_full Global Attractor of Thermoelastic Coupled Beam Equations with Structural Damping
title_fullStr Global Attractor of Thermoelastic Coupled Beam Equations with Structural Damping
title_full_unstemmed Global Attractor of Thermoelastic Coupled Beam Equations with Structural Damping
title_sort global attractor of thermoelastic coupled beam equations with structural damping
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2017-01-01
description In this paper, we study the existence of a global attractor for a class of n-dimension thermoelastic coupled beam equations with structural damping utt+Δ2u+Δ2ut-[σ(∫Ω‍(∇u)2dx)+ϕ(∫Ω‍∇u∇utdx)]Δu+f1(u)+g(ut)+νΔθ=q(x),  in  Ω×R+, and θt-Δθ+f2(θ)-νΔut=0. Here Ω is a bounded domain of RN, and σ(·) and ϕ(·) are both continuous nonnegative nonlinear real functions and q is a static load. The source terms f1(u) and f2(θ) and nonlinear external damping g(ut) are essentially |u|ρu, |θ|ϱθ, and |ut|rut respectively.
url http://dx.doi.org/10.1155/2017/2908964
work_keys_str_mv AT peirongshi globalattractorofthermoelasticcoupledbeamequationswithstructuraldamping
AT danxiawang globalattractorofthermoelasticcoupledbeamequationswithstructuraldamping
AT weiyichen globalattractorofthermoelasticcoupledbeamequationswithstructuraldamping
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