Session VII:

Abstract

In this paper we are concerned with Kirchhoff equations with strong damping and quasi-periodic external forcing on arbitrary flat tori. Such models arise from nonlinear forced vibrations of multidimensional bodies in which the dependence of the tension on the deformation cannot be neglected. We establish the existence of quasi-periodic traveling waves whose frequency is consistent with that of the forcing term. Due to strong damping, we don't impose any non-resonance conditions. Our arguments provide a general framework for studying singular perturbation problems with strong damping.