This paper develops a unified method to derive decay estimates for general second order integro-differential 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 -> +infinity. 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. (C) 2007 Elsevier Inc. All rights reserved.
Decay estimates for second order evolution equations with memory / Fatiha Alabau, Boussouira; Piermarco, Cannarsa; Sforza, Daniela. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - ELETTRONICO. - 254:5(2008), pp. 1342-1372. [10.1016/j.jfa.2007.09.012]