Nova S¶erie OPTIMAL ENERGY DECAY RATE OF COUPLED WAVE EQUATIONS

Abstract: We consider a system of coupled wave equations subject to positive vis-cous damping. Under the assumption that the damping function is of bounded variations, we give the asymptotic expansion of eigenvalues and eigenfunctions of the in¯nitesimal generator of the associated semigroup. Moreover, we prove that the eigenfunctions form a Riesz basis in the energy space.