Uniform rates of decay of solutions for a nonlinear lattice with memory

Abstract

In this paper we study a nonlinear lattice with memory and show that the problem is globally well posed. Furthermore we find uniform rates of decay of the total energy. Our main result shows that the memory effect is strong enough to produce a uniform rate of decay. That is, if the relaxation function decays exponentially then, the corresponding solution also decays exponentially. When the relaxation kernel decays polynomially then, the solution also decays polynomially as time goes to infinity.