Large time dynamics of a nonlinear spring-mass-damper model

In this paper we consider a nonlinear strongly damped wave equation as a model for a controlled spring-mass-damper system and give some results concerning its large time behaviour. It can be seen that the infinite dimensional system admits a two-dimensional attracting manifold where the equation is...

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Bibliographic Details
Published in:Nonlinear analysis 2008-11, Vol.69 (9), p.3110-3127
Main Author: Pellicer, Marta
Format: Article
Language:English
Online Access:Get full text
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Summary:In this paper we consider a nonlinear strongly damped wave equation as a model for a controlled spring-mass-damper system and give some results concerning its large time behaviour. It can be seen that the infinite dimensional system admits a two-dimensional attracting manifold where the equation is well represented by a classical nonlinear oscillations ODE, which can be exhibited explicitly. In contrast to other papers, this one applies Invariant Manifold Theory to a problem whose linear part is not self-adjoint.
ISSN:0362-546X
DOI:10.1007/b98103