Plates with Boundary Damping
In this chapter we consider models where the main source of dissipation is generated by boundary damping. Typical physical examples include boundary friction applied to an edge of the plate. This type of problem—with geometrically constrained support of the damping—is mathematically more demanding. Indeed, the dissipation is active on a much more restrictive support, hence potentially less effective. However, recent developments in the area of boundary stabilization of plates provide new tools in order to carry out the appropriate estimates. These are based on a multipliers method and microlocal analysis estimates. We first consider models with the rotational inertia included. These problems are more tractable and simpler, due to the fact that the nonlinear term acts upon the system as a compact perturbation. Proving asymptotic smoothness in that case is an easier task. When the rotational inertia are absent in the model, the analysis is more involved and delicate, because it involves the need for compensating the lack of compactness.
KeywordsStrong Solution Global Attractor Rotational Inertia Free Boundary Condition Energy Inequality
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