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 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.