Global attractor of thermoelastic coupled beam equations with structural damping
type: Item
instance of: scholarly article
title: Global attractor of thermoelastic coupled beam equations with structural damping
zbMATH Open document ID: 1426.74192
DOI: 10.1155/2017/2908964
author: Peirong Shi
author: Danxia Wang
author: Wei-Yi Chen
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: In this paper, we study the existence of a global attractor for a class of \(n\)-dimension thermoelastic coupled beam equations with structural damping \(u_{t t} + \Delta^2 u + \Delta^2 u_t - [\sigma(\int_{\Omega} (\nabla u)^2 d x) + \phi(\int_{\Omega} \nabla u \nabla u_t d x)] \Delta u + f_1(u) + g(u_t) + \nu \Delta \theta = q(x)\), in \(\Omega \times R^+\), and \(\theta_t - \Delta \theta + f_2(\theta) - \nu \Delta u_t = 0\). Here \(\Omega\) is a bounded domain of \(R^N\), and \(\sigma(\cdot)\) and \(\phi(\cdot)\) are both continuous nonnegative nonlinear real functions and \(q\) is a static load. The source terms \(f_1(u)\) and \(f_2(\theta)\) and nonlinear external damping \(g(u_t)\) are essentially \(| u |^\rho u, | \theta |^{\varrho} \theta \), and \(| u_t |^r u_t\) respectively.
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 6971921
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/2908964
OpenAlex ID: W2601690653
Wikidata QID: Q59147435
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description: scientific article; zbMATH DE number 6971921