Spectral asymptotics for the vectorial damped wave equation

The eigenfrequencies associated to a scalar damped wave equation are known to belong to a band parallel to the real axis. In [Sj{\"o}00] J. Sj{\"o}strand showed that up to a set of density 0, the eigenfrequencies are confined in a thinner band determined by the Birkhoff limits of the dampi...

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Veröffentlicht in:arXiv.org 2021-11
1. Verfasser: Klein, Guillaume
Format: Artikel
Sprache:eng
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Zusammenfassung:The eigenfrequencies associated to a scalar damped wave equation are known to belong to a band parallel to the real axis. In [Sj{\"o}00] J. Sj{\"o}strand showed that up to a set of density 0, the eigenfrequencies are confined in a thinner band determined by the Birkhoff limits of the damping term. In this article we show that this result is still true for a vectorial damped wave equation. In this setting the Lyapunov exponents of the cocycle given by the damping term play the role of the Birkhoff limits of the scalar setting.
ISSN:2331-8422