The hypocoercivity index for the short time behavior of linear time-invariant ODE systems

Franz Achleitner; Anton Arnold; Eric A. Carlen

doi:10.1016/j.jde.2023.06.027

paper

The hypocoercivity index for the short time behavior of linear time-invariant ODE systems

arXiv:2109.10784 · doi:10.1016/j.jde.2023.06.027

Abstract

We consider the class of conservative-dissipative ODE systems, which is a subclass of Lyapunov stable, linear time-invariant ODE systems. We characterize asymptotically stable, conservative-dissipative ODE systems via the hypocoercivity (theory) of their system matrices. Our main result is a concise characterization of the hypocoercivity index (an algebraic structural property of matrices with positive semi-definite Hermitian part introduced in Achleitner, Arnold, and Carlen (2018)) in terms of the short time behavior of the propagator norm for the associated conservative-dissipative ODE system.