Semigroup decay for the wave equation with unbounded damping
Analysis of PDEs
2026-03-24 v1 Mathematical Physics
Functional Analysis
math.MP
Abstract
We study the damped wave equation with a damping coefficient which is possibly singular and unbounded at infinity. In general, zero belongs to the spectrum of the corresponding generator, which prevents a uniform (exponential) decay for the energy. However, for initial conditions in a suitable subspace, a detailed analysis of the resolvent norm for low frequencies leads to sharp polynomial time-decay rates for the solution and its energy.
Cite
@article{arxiv.2603.21805,
title = {Semigroup decay for the wave equation with unbounded damping},
author = {Antonio Arnal and Borbala Gerhat and Julien Royer and Petr Siegl},
journal= {arXiv preprint arXiv:2603.21805},
year = {2026}
}