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

被引：3

作者：

Achleitner, Franz ^{[1
]}

Arnold, Anton ^{[1
]}

Carlen, Eric A. ^{[2
]}

机构：

[1] TU Wien, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

[2] Rutgers State Univ, Dept Math, 110 Frelinghuysen Rd, Piscataway, NJ 08854 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 371卷

基金：

奥地利科学基金会;

关键词：

Semi-dissipative ODE systems; Hypocoercivity (index); EQUATIONS; NORMS;

D O I：

10.1016/j.jde.2023.06.027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. & COPY; 2023 Elsevier Inc. All rights reserved.

引用

页码：83 / 115

页数：33

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