Asymptotic stability of the wave equation on compact surfaces and locally distributed damping - A sharp result

TL;DR

This paper investigates the asymptotic stability of the wave equation on compact surfaces with damping applied in small, well-chosen regions, providing sharp results on stability conditions.

Contribution

It offers a precise characterization of stability when damping is localized on small subsets of the surface, extending previous results to more general geometries.

Findings

Stability achieved with damping on arbitrarily small regions

Sharp conditions for asymptotic stability established

Extension to general compact surfaces

Abstract

This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping. We study the case where the damping is effective in a well-chosen subset of arbitrarily small measure.