Reachability of a second-order integro-differential equation on Riemannian manifold for a viscoelasticity mod

Abstract

We study a reachability problem for a second-order integro-differential equation on a finite-dimensional Riemannian manifold, which is a model equation for viscoelasiticity. We apply a Carleman estimate for the wave equations on Riemannian manifolds to establish the observability inequality.