The decay of solutions of a wave equation with memory

Abstract

In this paper the qualitative behaviour of a damped linear wave equation with memory is studied. A new energy functional is introduced which generalizes some of the most common energy functionals found in the literature for this type of problem. We establish an upper bound for this functional that, under suitable regularity conditions, converges to zero as time increases. Numerical waves that mimic their continuous counterpart are also computed using the finite element approach.