[Back]

A. Arnold, A. Einav, T. Wöhrer:
"On the rates of decay to equilibrium in degenerate and defective Fokker-Plnack equations";
in: "ASC Report 18/2017", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2017, ISBN: 978-3-902627-10-0, 1 - 27.

We establish sharp long time asymptotic behaviour for a family of entropies to defective Fokker-Planck equations and show that, much like de-fective finite dimensional ODEs, their decay rate is an exponential multiplied by a polynomial in time. The novelty of our study lies in the amalgamation of spectral theory and a quantitative non-symmetric hypercontractivity result, as opposed to the usual approach of the entropy method.

Fokker-Planck equations, Spectral Theory, non-symmetric hypercon-tractivity, long time behaviour.

http://www.asc.tuwien.ac.at/preprint/2017/asc18x2017.pdf