Corpus ID: 237592779

The hypocoercivity index for the short and large time behavior of ODEs

@inproceedings{Achleitner2021TheHI,
  title={The hypocoercivity index for the short and large time behavior of ODEs},
  author={Franz Achleitner and Anton Arnold and Eric A. Carlen},
  year={2021}
}
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 [2]) in terms of the short time behavior of the… Expand

Figures from this paper

Hypocoercivity and controllability in linear semi-dissipative ODEs and DAEs
A detailed analysis of the stability of dynamical systems of evolution equations (finite or infinite-dimensional) is still very problem dependent and computationally challenging, see [6, 18, 19, 27].Expand
Hypocoercivity and controllability in linear semi-dissipative Hamiltonian ODEs and DAEs
For the classes of finite dimensional linear time-invariant semi-dissipative Hamiltonian ordinary differential equations and differential-algebraic equations, stability and hypocoercivity areExpand
Sharpening of decay rates in Fourier based hypocoercivity methods
This paper is dealing with two $L^2$ hypocoercivity methods based on Fourier decomposition and mode-by-mode estimates, with applications to rates of convergence or decay in kinetic equations on theExpand
Propagator norm and sharp decay estimates for Fokker-Planck equations with linear drift
We are concerned with the short- and large-time behavior of the $L^2$-propagator norm of Fokker-Planck equations with linear drift, i.e. $\partial_t f=\mathrm{div}_{x}{(D \nabla_x f+Cxf)}$. With aExpand

References

SHOWING 1-10 OF 21 REFERENCES
Hypocoercivity and controllability in linear semi-dissipative ODEs and DAEs
A detailed analysis of the stability of dynamical systems of evolution equations (finite or infinite-dimensional) is still very problem dependent and computationally challenging, see [6, 18, 19, 27].Expand
On Optimal Decay Estimates for ODEs and PDEs with Modal Decomposition
We consider the Goldstein-Taylor model, which is a 2-velocity BGK model, and construct the "optimal" Lyapunov functional to quantify the convergence to the unique normalized steady state. TheExpand
On linear hypocoercive BGK models
We study hypocoercivity for a class of linear and linearized BGK models for discrete and continuous phase spaces. We develop methods for constructing entropy functionals that prove exponential ratesExpand
Stability Radii for Linear Hamiltonian Systems with Dissipation Under Structure-Preserving Perturbations
TLDR
It is shown that under structure-preserving perturbations the asymptotical stability of a DH system is much more robust than under general perturbation, since the distance to instability can be much larger when struc... Expand
Sharp decay estimates in local sensitivity analysis for evolution equations with uncertainties: From ODEs to linear kinetic equations
We review the Lyapunov functional method for linear ODEs and give an explicit construction of such functionals that yields sharp decay estimates, including an extension to defective ODE systems. AsExpand
Sharp entropy decay for hypocoercive and non-symmetric Fokker-Planck equations with linear drift
We investigate the existence of steady states and exponential decay for hypocoercive Fokker--Planck equations on the whole space with drift terms that are linear in the position variable. For thisExpand
HYPOCOERCIVITY FOR LINEAR KINETIC EQUATIONS CONSERVING MASS
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collisionExpand
Large-time behavior in non-symmetric Fokker-Planck equations
We consider three classes of linear non-symmetric Fokker-Planck equations having a unique steady state and establish exponential convergence of solutions towards the steady state with explicitExpand
Étude spectrale minutieuse de processus moins indécis que les autres
In this paper we are looking for quantitative estimates for the convergene to equilibrium of non reversible Markov processes, especialy in short times. The models studied are simple enough to get anExpand
Hypoelliptic second order differential equations
that is, if u must be a C ~ function in every open set where Pu is a C ~ function. Necessary and sufficient conditions for P to be hypoelliptic have been known for quite some time when theExpand
...
1
2
3
...