Well-posedness and stability of a hinged plate equation with a localized nonlinear structural damping Original Research Article

We consider an NN-dimensional plate equation in a bounded domain with a locally distributed nonlinear dissipation involving the Laplacian. The dissipation is effective in a neighborhood of a suitable portion of the boundary. When the space dimension equals two, the associated linear equation corresponds to the plate equation with a localized viscoelastic (or structural) damping. First we prove existence, uniqueness, and smoothness results. Then, using an appropriate perturbed energy coupled with multiplier technique, we directly prove exponential and polynomial decay estimates for the underlying energy. To the author’s best knowledge, the perturbed energy approach is new in the framework of stabilization of second order evolution equations with locally distributed damping.