Ali PERINA (LAMIA) : Stabilization of a transmission system between an elastic material and a Mindlin-Timoshenko plate.

In this presentation, we focus on the stabilization of a transmission system between a partially damped Mindlin-Timoshenko plate and an undamped elastic body. The two materials can be seen as part of a bounded domain, the plate being a neighborhood of the boundary and the elastic material being surrounded by the plate. We have the usual transmission conditions at the interface. The damping only appears in the equations describing the motion of the angles of rotation of a filament. We demonstrate that if the propagation velocities of the waves due to the plate are equal, while the Lamé constants of the elastic material are greater than or equal to those of the plate, then this system is exponentially stable. All else being equal, if the wave velocities due to the plate are distinct, then this system is polynomially stable. These results improve on those of Mindlin-Timoshenko plate stabilization with linear frictional damping.