Decay estimates for second order evolution equations with memory

This paper develops a unified method to derive decay estimates for general second order integrodifferential evolution equations with semilinear source terms. Depending on the properties of convolution kernels at infinity, we show that the energy of a mild solution decays exponentially or polynomially as t →+∞. Our approach is based on integral inequalities and multiplier techniques. These decay results can be applied to various partial differential equations. We discuss three examples: a semilinear viscoelastic wave equation, a linear anisotropic elasticity model, and a Petrovsky type system. © 2007 Elsevier Inc. All rights reserved