Shock structure in viscoelasticity of relaxation type

We are concerned with the shock structure in viscoelasticity of rate type. The existence of a shock profile, which in the vanishing relaxation limit becomes an elastic shock, is demonstrated by an explicit construction of the solution of viscoelastic equations provided that the equilibrium stress-strain relation is governed by a parabolic law. For a more general stress-strain law which does not differ substantially from a parabolic one, the solution is obtained from a perturbation expansion.