Tue, 29 May 2018
17:00
17:00
C1
On the decay rate for the wave equation with viscoelastic boundary damping
Reinhard Stahn
(Technical University of Dresden)
We consider a vector-valued function $f: \mathbb{R}_+ \to X$ which is locally of bounded variation and give a decay rate for $|A(t)|$ for increasing $t$ under certain conditions on the Laplace-Stieltjes transform $\widehat{dA}$ of $A$. For this, we use a Tauberian condition inspired by the work of Ingham and Karamata and a contour integration method invented by Newman. Our result is a generalisation of already known Tauberian theorems for bounded functions and is applicable to Dirichlet series. We will say something about the connection between the obtained decay rates and number theory.