Stabilization of the wave equation with Ventcel boundary condition

We consider a damped wave equation on a open subset of Rn or a smooth Riemannian manifold with boundary, with Ventcel boundary conditions, with a linear damping, acting either in the interior or at the boundary. This equation is a model for a vibrating structure with a layer with higher rigidity of thickness delta> 0. By means of a proper Carleman estimate for second-order elliptic operators near the boundary, we derive a resolvent estimate for the wave semigroup generator along the imaginary axis, which in turn yields the logarithmic decay rate of the energy. This stabilization result is obtained uniformly in delta. (C) 2016 Elsevier Masson SAS. All rights reserved.