Finite-dimensional behaviour of a nonautonomous partial differential equation: Forced oscillations of an extensible beam
type: Item
instance of: scholarly article
title: Finite-dimensional behaviour of a nonautonomous partial differential equation: Forced oscillations of an extensible beam
zbMATH Open document ID: 0773.35077
author: Eduard Feireisl
published in: Journal of Differential Equations
publication date: 1993-05-16T00:00:00Z
review text: We prove the existence of a finite-dimensional attractor for the nonautonomous equation: \[ U_{tt}+ dU_ t+ aU_{xxxx}+ \left( K(t)- \int_ 0^ \pi U_ z^ 2(z,t)dz\right) U_{xx}=f(x,t), \tag{1} \] \(U(0,t)=U(\pi,t)=U_{xx}(0,t)=U_{xx}(\pi,t)=0\), where \(K\) and \(f\) are time periodic with periods \(\omega_ 1\), \(\omega_ 2\). The equation (1) represents a model of transversal motion of a hinged beam where the external damping is proportional to the velocity.
reviewed by: Eduard Feireisl
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 34D45
zbMATH DE Number: 166902
zbMATH Keywords: existence of a finite-dimensional attractor
zbMATH Keywords: transversal motion of a hinged beam
MaRDI profile type: Publication
Wikidata QID: Q59316837
full work available at URL: jdeq.1993.1014
OpenAlex ID: W1973736381
DOI: 10.1006/JDEQ.1993.1014
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description: scientific article; zbMATH DE number 166902