Sharp Polynomial Decay for Polynomially Singular Damping on the Torus

Authors

Perry Kleinhenz, Illinois State UniversityFollow
Ruoyu P.T. Wang, Yale University

Document Type

Article

Publication Title

Annals of PDE

Publication Date

2026

Keywords

damped waves, singular damping, backward uniqueness, Schrödinger observability

Abstract

We study energy decay rates for the damped wave equation with unbounded damping, without the geometric control condition. Our main decay result is sharp polynomial energy decay for polynomially controlled singular damping on the torus. We also prove that for normally L^p-damping on compact manifolds, the Schrödinger observability gives p-dependent polynomial decay, and finite time extinction cannot occur. We show that polynomially controlled singular damping on the circle gives exponential decay.

Funding Source

PBK is partially supported by NSF grant DMS-2530465. RPTW is partially supported by NSF grant DMS-2054424. This article was published Open Access thanks to a transformative agreement between Milner Library and Springer Nature.

Comments

First published in Annals of PDE (2026): https://doi.org/10.1007/s40818-025-00230-2. Supplemental information freely available on the publisher's site.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

DOI

10.1007/s40818-025-00230-2

Recommended Citation

Kleinhenz, P., Wang, R.P.T. Sharp Polynomial Decay for Polynomially Singular Damping on the Torus. Ann. PDE 12, 6 (2026). https://doi.org/10.1007/s40818-025-00230-2