Existence and asymptotic behaviour of solutions for a class of quasi-linear evolution equations with non-linear damping and source terms

We consider a class of quasi-linear evolution equations with non-linear damping and source terms arising from the models of non-linear viscoelasticity. By a Galerkin approximation scheme combined with the potential well method we prove that when m<p, where m(greater than or equal toO) and p are, respectively, the growth orders of the non-linear strain terms and the source term, under appropriate conditions, the initial boundary value problem of the above-mentioned equations admits global weak solutions and the solutions decay to zero as t-->infinity. Copyright (C) 2002 John Wiley Sons, Ltd.