Vorträge und Posterpräsentationen (ohne Tagungsband-Eintrag):
F. Achleitner:
"Short- and long-time behavior in (hypo)coercive ODE-systems and kinetic partial differential equations";
Vortrag: DMV-ÖMG Annual Conference 2021,
Passau, Deutschland (eingeladen);
27.09.2021
- 01.10.2021.
Kurzfassung deutsch:
see english abstract
Kurzfassung englisch:
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.
Schlagworte:
Kinetic equations, BGK models, hypocoercivity, Lyapunov functionals, perturbation methods for matrix equations.
Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.