General decay rate estimates for viscoelastic dissipative systems

The linear viscoelastic equation is considered. We prove uniform decay rates of the energy by assuming a nonlinear feedback acting on the boundary, without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function. Our estimate depends both on the behavior of the damping term near zero and on the behavior of the relaxation function at infinity.The proofs are based on the multiplier method and on a general lemma about convergent and divergent series for obtaining the uniform decay rates.