The Multidimensional Wave Equation with Generalized Acoustic Boundary Conditions II: Polynomial Stability

Abstract

We study the wave equation on a domain of $\mathbb{R}^d$, $d\geq 2$, with dynamical boundary control applied on a part of the boundary and a Dirichlet boundary condition on the remaining part. We prove the polynomial stability of our model by two different methods: the resolvent and multiplier methods. Some illustrative examples are presented.