Coupled second order semilinear evolution equations indirectly damped via memory effects

In this paper, we study a system of coupled second order semilinear evolution equations in a Hilbert space, which is partially damped through memory effects. A global existence and uniqueness theorem regarding the solutions to its Cauchy problem is given. Following this, we analyze stability of the system energy, and obtain various decay rates corresponding to the integral kernel, some of them being optimal. Moreover, we apply our abstract theory to concrete systems, including that of Timoshenko type, for which we essentially improve the previous related results.