Decay rates for the energy of a singular nonlocal viscoelastic system

This work deals with decay rates for the energy of an initial boundary value problem with a nonlocal boundary condition for a system of nonlinear singular viscoelastic equations. We prove the decay rates for the energy of a singular one-dimensional viscoelastic system with a nonlinear source term and nonlocal boundary condition of relaxation kernels described by the inequalitygi ' mml:mfenced close=")" open="(" separators=""t <=-H mml:mfenced close=")" open="(" separators="gi mml:mfenced close=")" open="(" separators="t,<mml:mfenced close=")" open="(" separators=""i=1,2for allt >= 0, withHconvex.