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-[26-28] 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. (C) 2016 Elsevier Inc. All rights reserved.