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arXiv · 2302.04498

A remark on the logarithmic decay of the damped wave and Schr\"odinger equations on a compact Riemannian manifold

Iván Moyano·Nicolas Burq
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Abstract

In this paper we consider a compact Riemannian manifold (M, g) of class C 1 $\cap$ W 2,$\infty$ and the damped wave or Schr\"odinger equations on M , under the action of a damping function a = a(x). We establish the following fact: if the measure of the set {x $\in$ M ; a(x) = 0} is strictly positive, then the decay in time of the associated energy is at least logarithmic.

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Iván Moyano, Nicolas Burq. 2023-02-09. A remark on the logarithmic decay of the damped wave and Schr\"odinger equations on a compact Riemannian manifold. https://arxiv.org/abs/2302.04498

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