LOCAL INDIRECT STABILIZATION OF SAME COUPLED EVOLUTION SYSTEMS THROUGH RESOLVENT ESTIMATES

In this paper, we consider same systems of two coupled equations (wave-wave, Schro center dot dinger-Schro center dot dinger) in a bounded domain. Only one of the two equations is directly damped by a localized damping term (indirect stabilization). Under geometric control conditions on both coupling and damping regions (internal or boundary), we establish the energy decay rate by means of a suitable resolvent estimate. The numerical contribution is interpreted to confirm the theoretical result of a wave-wave system.