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 $t^{ -\frac{ 1}{ 2}}$ if the two waves have the same speed of propagation, and with rate $t^{ -\frac{ 1}{ 3}}$ 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 $t^{ -1}$.
Categories: math.AP