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STABILIZATION OF THE NONLINEAR DAMPED WAVE EQUATION VIA LINEAR WEAK OBSERVABILITY

Bchatnia Ahmed, 2016

Nonlinear Differential Equations and Applications , 1, 1, 1-17, Janvier 2016

Résumé

We consider the problem of energy decay rates for nonlinearly damped abstract infinite dimensional systems. We prove sharp, simple and quasi-optimal energy decay rates through an indirect method, namely a weak observability estimate for the corresponding undamped system. One of the main advantage of these results is that they allow to combine the optimalweight

convexity method of [3, Alabau-Boussouira] and a methodology of [6,Ammari-Tucsnak] for weak stabilization by observability. Our results extend to nonlinearly damped systems, those of Ammari and Tucsnak [6]. At the end, we give an appendix on the weak stabilization of linear evolution systems.

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