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arXiv · 2111.05580

Energy decay for a system of Schr{\"o}dinger equations in a wave guide

Radhia Ayechi·Ilhem Boukhris·Julien Royer
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Abstract

We prove exponential decay for a system of two Schr{\"o}dinger equations in a wave guide, with coupling and damping at the boundary. This relies on the spectral analysis of the corresponding coupled Schr{\"o}dinger operator on the one-dimensional cross section. We show in particular that we have a spectral gap and that the corresponding generalized eigenfunctions form a Riesz basis.

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Radhia Ayechi, Ilhem Boukhris, Julien Royer. 2021-11-10. Energy decay for a system of Schr{\"o}dinger equations in a wave guide. https://arxiv.org/abs/2111.05580

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