Global attractors for degenerate partial differential equations from nonlinear viscoelasticity (Q5940268)

The authors consider 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 PDE of this reduced problem has an attractor and that this attractor is contained in an invariant two-dimensional manifold. Here, the solutions are governed by the classical ODE for the forced motion of a particle on a massless spring.