ASYMPTOTIC EXPANSION OF WEAK SOLUTIONS OF THE DIRICHLET PROBLEM FOR A NONLINEAR VISCOELASTIC WAVE EQUATION WITH BALARISHNAN-TAYLOR TERM

Abstract

In this paper, we consider the Dirichlet problem for a nonlinear viscoelastic wave equation with Balakrishnan-Taylor damping. First, under suitable conditions on the initial data, the local existence and uniqueness of a weak solution are established by the linearization method together with the Faedo-Galerkin method. Next, when the source term and Balakrishnan-Taylor term contain noise parameters, an expansion an asymptotic expansion of solutions on this small parameter with second order is established.