Spectral asymptotics for the vectorial damped wave equation
Analysis of PDEs
2021-11-18 v1 Optimization and Control
Abstract
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.
Keywords
Cite
@article{arxiv.2111.08982,
title = {Spectral asymptotics for the vectorial damped wave equation},
author = {Guillaume Klein},
journal= {arXiv preprint arXiv:2111.08982},
year = {2021}
}