Spatial estimates for Kelvin-Voigt finite elasticity with nonlinear viscosity: well behaved solutions in space.

Abstract

We provide some spatial estimates for the nonlinear partial di erential equation governing anti-plane motions in a nonlinear viscoelastic theory of Kelvin-Voigt type when the viscosity is a function of the strain rate. The spatial estimates we prove are an alternative of Phragmen-Lindel of type. These estimates are possible when a precise balance between the elastic and viscoelastic nonlinearities holds