Polynomial Stability of an Elastic Plate with Dynamical Boundary Control

This work studies the boundary feedback stabilization for an elastic thin plate, where one part of its boundary is clamped and the remaining free part is attached to a rigid body. The boundary feedback controls are applied to the free boundary. Given that the boundary of the domain may have corners, we introduce a proper abstract framework to analyze the well-posedness and estimate the resolvent. When the geometric control condition (GCC) holds, we prove a polynomial energy decay rate of t -1/2 . For cases where GCC does not hold, we analyze the system on a rectangular domain with control applied to only one edge and obtain a slower decay rate t -1/3 .