Stabilisation of Waves on Product Manifolds by Boundary Strips

TL;DR

This paper demonstrates that boundary damping can ensure wave decay on product manifolds and provides a method to relate impedance problem estimates to wave decay.

Contribution

It introduces a general scheme linking resolvent estimates for impedance problems to wave decay on product manifolds, expanding understanding of wave stabilization.

Findings

Boundary damping strips can ensure wave decay.

A scheme to connect impedance estimates to wave decay.

Wave decay rate of t^{-1/2} achieved under certain conditions.

Abstract

We show that a transversely geometrically controlling boundary damping strip is sufficient but not necessary for $t^{-1/2}$-decay of waves on product manifolds. We give a general scheme to turn resolvent estimates for impedance problems on cross-sections to wave decay on product manifolds.