Exponential stability in mean–square of parabolic quasilinear stochastic delay evolution equations

Abstract

We initiate a study on the exponential stability of a parabolic quasi linear stochastic evolution equation with a variable delay which nay be regarded as a perturbed quasi linear differential systen. We first obtain the existence and uniqueness of a strong solution. Next, we establish exponential stability of a strong solution in the following sense: if the unperturbed systen is exponentially stable and the perturbation is small enough, then the perturbed equation renains exponentially stable