Global attractors for degenerate partial differential equations from nonlinear viscoelasticity

We study several problems for the forced motion of light, uniform, nonlinearly viscoelastic bodies carrying heavy attachments. A ‘reduced’ problem for such motions is obtained by setting the ratio of the inertia of the viscoelastic body to the inertia of the attachment equal to zero. Using methods from infinite-dimensional dynamical systems theory, we prove that the degenerate partial differential equation of this reduced problem has an attractor and that this attractor is contained in an invariant two-dimensional manifold on which solutions are governed by the classical ordinary differential equation for the forced motion of a particle on a massless spring.