Stability of Mindlin-Timoshenko plate with nonlinear boundary damping and boundary sources

Presented here is a study of long-term behavior of Mindlin-Timoshenko (RMT) plate systems, focusing on the interplay between nonlinear viscous boundary damping and boundary source terms. This work complements [28] which established local well-posedness of this problem, and global well-posedness when the boundary damping dominates the boundary sources (in an appropriate sense). The current paper develops the potential well theory for the RMT system: global existence for potential well solutions without restricting the boundary source exponents, and explicit energy decay rates dependent on the boundary damping exponents. This work along with [26], [27], [28] provides the fundamental well-posedness and stability theory for MT plates under the interplay of damping and source terms acting either in the interior or on the boundary of the plate.