Generic simplicity of the spectrum and stabilization for a plate equation

In this work we prove the generic simplicity of the spectrum of the clamped plate equation in a bounded regular domain of R-d. That is, given Omega su bset of R-d, we show that there exists an arbitrarily small deformation of the domain u, such that all the eigenvalues of the plate system in the defo rmed domain Omega + u are simple. To prove this result we first prove a non standard unique continuation property for this system that also holds gener ically with respect to the perturbations of the domain. Both the proof of t his generic uniqueness result and the generic simplicity of the spectrum us e Baire's lemma and shape differentiation. Finally, we show an application of this unique continuation property to a result of generic stabilization f or a plate system with one dissipative boundary condition.