Orateur
Description
We study a class of abstract linear systems which can especially be used to represent wave equations and other hyperbolic partial differential equations with damping. Our main interest is in formulating sufficient conditions which guarantee that the energy of the solutions of the system decays to zero asymptotically, and in estimating the decay rate of the energy. In studying both the stability and the existence of solutions of our models we employ a control-theoretic viewpoint which allows us to see the damped system as a closed-loop system arising from an undamped model under negative feedback. This in particular naturally connects the stability analysis of the damped model to the observability properties of the undamped open-loop system. We present recent results on the polynomial and non-uniform stability of the damped system. Finally, we introduce new results on well-posedness and asymptotic stability for a class of nonlinear dampings.
The presentation is based on joint work with R. Chill, A. Hastir, D. Seifert, R. Stahn, Y. Tomilov, and N. Vanspranghe.
