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arXiv · 2510.00179

Integrated Local Energy Decay for Waves with Time-Dependent Damping

Perry Kleinhenz·Michael McNulty
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Abstract

We prove integrated local energy decay for solutions of the damped wave equation with time-dependent damping satisfying an appropriate generalization of the geometric control condition on asymptotically flat, stationary space-times. We first obtain a high frequency estimate, which we prove via a positive commutator estimate using an escape function explicitly constructed in terms of the damping around individual space-time trajectories. We combine the high frequency estimate with low and medium frequency results for the undamped problem, then we handle the damping term as a perturbation to obtain local energy decay.

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Perry Kleinhenz, Michael McNulty. 2025-09-30. Integrated Local Energy Decay for Waves with Time-Dependent Damping. https://arxiv.org/abs/2510.00179

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