Title: On the decay rate for the wave equation with viscoelastic boundary damping,
Abstract: We consider the wave equation with a boundary condition of memory type. Under
natural conditions on the acoustic impedance $\hat{k}$ of the boundary one can
define a corresponding semigroup of contractions (Desch, Fasangova, Milota,
Probst 2010). With the help of Tauberian theorems we establish energy decay
rates via resolvent estimates on the generator $-\mathcal{A}$ of the semigroup.
We reduce the problem of estimating the resolvent of $-\mathcal{A}$ to the
problem of estimating the resolvent of the corresponding stationary problem.
Under not too strict additional assumptions on $\hat{k}$ we establish an upper
bound on the resolvent. For the wave equation on the interval or the disk we
prove our estimates to be sharp.