Comparison arguments and decay estimates in non-linear viscoelasticity

In a recent paper two Phragmen-Lindelof growth-decay estimates were derived for solutions of initial boundary problems arising in anti-plane shear dynamic deformations in the non-linear theory of viscoelasticity. In particular the results apply to the sub-linear family of power-law materials. In this paper we improve the decay estimates. We prove that the rate of decay is bounded below by an exponential of a second degree polynomial of the distance from the end. The main tool is the use of the comparison methods in a similar way to their use for parabolic problems. (C) 2003 Elsevier Science Ltd. All rights reserved.