Achleitner, F., Arnold, A., & Carlen, E. (2023). The hypocoercivity index for the short time behavior of linear time-invariant ODE systems. Journal of Differential Equations, 371, 83–115. https://doi.org/10.1016/j.jde.2023.06.027
Hypocoercivity (index); Semi-dissipative ODE systems
en
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 norm of the matrix exponential for the associated conservative-dissipative ODE system.
