Hypocoercivity and controllability in linear semi-dissipative Hamiltonian ordinary differential equations and differential-algebraic equations

Abstract

For the classes of finite-dimensional linear time-invariant semi-dissipative Hamiltonian ordinary differential equations and differential-algebraic equations with constant coefficients, 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.