STABILIZATION OF COUPLED WAVE EQUATIONS WITH VISCOUS DAMPING ON CYLINDRICAL AND NON-REGULAR DOMAINS: CASES WITHOUT THE GEOMETRIC CONTROL CONDITION
Résumé
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 .
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