Hypocoercivity and controllability in linear semi-dissipative Hamiltonian ODEs and DAEs

TL;DR

This paper explores the stability and hypocoercivity of linear semi-dissipative Hamiltonian ODEs and DAEs, linking these properties to control theory and analyzing their solution behavior through staircase forms, with applications to infinite-dimensional flows.

Contribution

It introduces a framework connecting hypocoercivity and controllability in semi-dissipative Hamiltonian systems, including finite and infinite-dimensional cases.

Findings

Characterization of solution behavior via staircase forms.

Relation of hypocoercivity index to system stability.

Application to infinite-dimensional flow problems.

Abstract

For the classes of finite dimensional linear time-invariant semi-dissipative Hamiltonian ordinary differential equations and differential-algebraic equations, stability and hypocoercivity are discussed and related to concepts from control theory. On the basis of staircase forms the solution behavior is characterized and connected to the hypocoercivity index of these evolution equations. The results are applied to two infinite dimensional flow problems.