Boundary stabilization of weakly coupled hyperbolic systems by one control force

This work is concerned with the boundary stabilization of an abstract system of two coupled second order evolution equations by only one control force (this is the case of indirect damping). We show that under a condition on the operators of each equation and on the boundary feedback operator, the energy of smooth solutions of this system decays polynomially at ∞. We then apply this abstract result to some systems of partial differential equations (wave-wave systems).