Talks and Poster Presentations (without Proceedings-Entry):
F. Achleitner:
"Short- and long-time behavior in (hypo)coercive ODE-systems and kinetic equations";
Talk: Workshop "Entropy, Flows and Inequalities (EFI)",
Universite Dauphine (Paris, France);
2021-10-13
- 2021-10-15.
English abstract:
We will discuss hypocoercivity on the level of ODEs and devise a new way to construct strict Lyapunov functionals:
Systems of ODEs dx/dt = Ax with semi-dissipative matrix A (i.e. the Hermitian part of matrix A is negative semi-definite) are Lyapunov stable but not necessarily asymptotically stable.
There exist many equivalent conditions, to decide if the ODE system is asymptotically stable or not.
Some conditions allow to construct a strict Lyapunov functional in a natural way.
We will review these classical conditions/approaches and identify a "hypocoercivity index" which e.g. characterizes the short-time asymptotics of the propagator norm for semi-dissipative ODEs.
Finally, we apply these results to study the long-time behavior of (hypocoercive) nonlinear BGK-type model with constant collision frequency, and (kinetic) Fokker-Planck equations.
In particular, we will compare our strict Lyapunov functionals for the linear(ized) kinetic equations with other classical approaches.
German abstract:
see english abstract
Keywords:
Kinetic equations, BGK models, hypocoercivity, Lyapunov functionals, perturbation methods for matrix equations.
Created from the Publication Database of the Vienna University of Technology.