#### Abstract

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.

*DATE *

**Time:** 1:30 P.M.

**Location:** PPB 300