General decay of the solution energy in a viscoelastic equation with a nonlinear source

Abstract

In a bounded domain, we consider ut t - Δ u + ∫0t g (t - τ) Δ u d τ = | u |γ u, where γ > 0and g is a nonnegative and decaying function. We prove that, for certain class of relaxation functions and certain initial data, the rate of decay of energy is similar to that of g. This result improves earlier ones in the literature in which only the exponential and polynomial decay rates are considered. © 2007 Elsevier Ltd. All rights reserved.