2021/11/17 by Guillaume Klein, Klein, Guillaume
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations
paper · doi:10.48550/arxiv.2111.08982
openalex publication_date 2021/11/17 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
The eigenfrequencies associated to a scalar damped wave equation are known to belong to a band parallel to the real axis. In [Sjö00] J. Sjöstrand 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.