  In this paper, we consider a one-dimensional finite-memory Bresse system with
homogeneous Dirichlet-Neumann-Neumann boundary conditions. We prove some
general decay results for the energy associated with the system in the case of
equal and non-equal speeds of wave propagation under appropriate conditions on
the relaxation function. In addition, we show by giving an example that in the
case of equal speeds of wave propagation and for certain polynomially decaying
relaxation functions, our result gives an optimal decay rate in the sense that
the decay rate of the system is exactly the same as that of the relaxation
function considered.
