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Gilles Francfort, LPMTM, Univ. Paris-Nord
"Observability for the wave equation on a thin domain"
In this joint work with P. Gerard, the goal is to compute the limit energy density of solutions of the linear wave equation on a thin 3d-domain, when the wavelength of the Cauchy data is of the order of the thickness h of the domain. That computation permits in turn to obtain necessary and sufficient condition for the uniform (in h) observability of the solutions to the damped wave equation on such a domain, provided the damping is active near the lateral boundary of that domain. Observability means that the initial energy is controlled by the energy dissipated on some time interval [0,T]. Whether this is in turn equivalent to the uniform (in h) stabilization of those solutions, that is whether the energy decreases exponentially in time, uniformly in h, remains open at present.