Séminaire d'AnalyseStabilization of some second order evolution equations by feedback laws.
jeudi 11 décembre 2014 11:00 - Tours - Salle 1180 (Bât E2)
In this talk, we discuss the stabilization of some evolution equations by feedback laws. First, we consider the wave equation on a domain Ω of R d , d ≥ 1 with dynamical boundary control applied on a part of the boundary and a Dirichlet boundary condition on the remaining part. We then furnish in the case d = 1 sufficient conditions that guarantee a polynomial stability using a method that combines an observability inequality for the associated undamped problem with regularity results of the solution of the undamped problem with a specific right-hand side. In addition, the optimality of the decay is shown in some cases with the help of precise spectral results. For d ≥ 2, the domain of the associated operator is not compactly embedded into the energy space. Nevertheless, we find sufficient conditions that give the strong stability. Then, we discuss the non uniform stability as well as the polynomial stability by two different methods depending on the type of the considered domain. We moreover introduce a general framework of second order evolution equations with dynamical feedbacks and a method to study the stability of its energy