Polynomial Decay Rate for a Wave Equation with Weak Dynamic Boundary Feedback Laws
We consider the stabilization of the wave equation by weak dynamic boundary feedback laws at one extremity. This system is not uniformly stable but we prove a polynomial stability. Our method consists in combining an observability inequality for the associated undamped problem obtained via sharp spectral results with regularity results of the solution of the undamped problem with a specific right-hand side. The optimality of the decay is also shown again thanks to precise spectral results of the operator associated with the damped problem.