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arXiv · 2207.06260

Energy decay for the time dependent damped wave equation

Perry Kleinhenz
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Abstract

Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions decays at an exponential rate if the damping coefficient satisfies a time dependent analogue of the classical geometric control condition. Existing time dependent observability inequalities are improved by removing technical assumptions on the permitted initial data.

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Perry Kleinhenz. 2022-07-13. Energy decay for the time dependent damped wave equation. https://arxiv.org/abs/2207.06260

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