General decay of solutions of a wave equation with a boundary control of memory type

In this paper we consider a semilinear wave equation, in a bounded domain, where the memory-type damping is acting on a part of the boundary. We establish a general decay result, from which the usual exponential and polynomial decay rates are only special cases. Our work allows certain relaxation functions which are not necessarily of exponential or polynomial decay and, therefore, generalizes and improves earlier results in the literature.