Arbitrary Decay of Energy for a Viscoelastic Problem with Balakrishnan-Taylor Damping

In this paper we consider a viscoelastic problem with Balakrishnan-Taylor damping u(tt) - (a + b parallel to del u parallel to(2) + sigma(del u, del u(t))) Delta u + integral(t)(0) g(t - s)Delta u(s) ds = 0 with Dirichlet boundary condition. We establish a decay result of the energy of solutions for the problem without imposing the usual relation between the relaxation function g and its derivative. This result generalizes earlier ones to an arbitrary rate of decay, which is not necessarily of exponential or polynomial decay.