Weak solutions for a nonlinear system in viscoelasticity

Abstract

We consider a one-dimensional model problem for the motion of a viscoelastic material with fading memory governed by a quasilinear hyperbolic system of integrodifferential equations of Volterra type. For given Cauchy data in , we use the method of vanishing viscosity and techniques of compensated compactness to obtain the existence of a weak solution (in the class of bounded measurable functions) in a special case