Stabilization of Coupled Wave Equations with Viscous Damping on Cylindrical and Non-regular Domains: Cases Without the Geometric Control Condition

In this paper, we investigate the direct and indirect stability of locally coupled wave equations with local viscous damping on cylindrical and non-regular domains without any geometric control condition. If only one equation is damped, we prove that the energy of our system decays polynomially with the rate t(-1/2 )if the two waves have the same speed of propagation, and with rate t(-1/3) if the two waves do not propagate at the same speed. Otherwise, in case of two damped equations, we prove a polynomial energy decay rate of order t(-1).