In this paper, we consider a one dimensional elastic system with two
porous
structures and memory effects in both porous equations. We prove that the weak
dissipation generated by the memory terms produces a general rate of decay
depending on the kernels of the memory terms and the coefficients of the
system. Our result improves that of [6] obtained in the
presence of strong damping and thermal effect. Moreover, the general decay
that we obtained generalizes the previous results in the sense that
exponential and polynomial rates of decay are only special cases.