Geometry of wave damping on the torus
Analysis of PDEs
2025-10-03 v2 Mathematical Physics
math.MP
Abstract
Energy decay rates of damped waves on the torus depend on the behavior of the damping near the undamped region and on the geometry of the damped set. In this paper we refine these geometric considerations, by introducing the concept of order of a glancing undamped point, and estimating decay rates in terms of this order. The proof is based on generalizing an averaging argument due to Sun. We also show that damping sets which attain these improvements are generic among polygons and smooth curves.
Cite
@article{arxiv.2509.05239,
title = {Geometry of wave damping on the torus},
author = {Kiril Datchev and Perry Kleinhenz and Antoine Prouff},
journal= {arXiv preprint arXiv:2509.05239},
year = {2025}
}
Comments
29 pages, 9 figures, version 2 adding acknowledgements and missing references to earlier work