Exponential stabilization of magnetoelastic waves in a Mindlin–Timoshenko plate by localized internal damping

Abstract

This article is a continuation of our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047–1065, 2012) on the polynomial stabilization of a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin–Timoshenko plate. We introduce nonlinear damping that is effective only in a small portion of the interior of the plate. It turns out that the model is uniformly exponentially stable when the function \({{{\mathbf{p}}}({\mathbf{x}},{\mathbf{U}}_t)}\), that represents the locally distributed damping, behaves linearly near the origin. However, the use of Mindlin–Timoshenko plate theory in the model enforces a restriction on the region occupied by the plate.