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arXiv · 2603.21805

Semigroup decay for the wave equation with unbounded damping

Antonio Arnal·Borbala Gerhat·Julien Royer·Petr Siegl
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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.

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Antonio Arnal, Borbala Gerhat, Julien Royer, Petr Siegl. 2026-03-23. Semigroup decay for the wave equation with unbounded damping. https://arxiv.org/abs/2603.21805

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