Stability of the Kirkhoff plate with nonlinear dissipative feedback acting as a bending moment

The author considers the Kirkhoff plate model defined on a bounded domain Ω in R² with nonlinear dissipation occurring in the bending moment acting on the boundary Γ. Specifically, an analysis is made of the asymptotic stability of the solutions to the classical equation of a thin, isotropic, homogeneous plate with nonlinear dissipation occurring on a portion of the edge of the plate. Under certain geometric conditions imposed on Ω, the author proves that the solutions decay to zero, when t→∞, in the natural energy norm