Semigroup decay for the wave equation with unbounded damping

Fuente: arXiv
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Bibliographic Details
Main Authors: Arnal, Antonio, Gerhat, Borbala, Royer, Julien, Siegl, Petr
Format: Preprint
Published: 2026
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author Arnal, Antonio
Gerhat, Borbala
Royer, Julien
Siegl, Petr
author_facet Arnal, Antonio
Gerhat, Borbala
Royer, Julien
Siegl, Petr
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2603_21805
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Semigroup decay for the wave equation with unbounded damping
Arnal, Antonio
Gerhat, Borbala
Royer, Julien
Siegl, Petr
Analysis of PDEs
Mathematical Physics
Functional Analysis
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.
title Semigroup decay for the wave equation with unbounded damping
topic Analysis of PDEs
Mathematical Physics
Functional Analysis
url https://arxiv.org/abs/2603.21805