On the rates of decay to equilibrium in degenerate and defective Fokker-Planck equations
Abstract
We establish sharp long time asymptotic behaviour for a family of entropies to defective Fokker-Planck equations and show that, much like defective 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.
- Publication:
-
Journal of Differential Equations
- Pub Date:
- June 2018
- DOI:
- 10.1016/j.jde.2018.01.052
- arXiv:
- arXiv:1709.10216
- Bibcode:
- 2018JDE...264.6843A
- Keywords:
-
- primary;
- 35Q84;
- 35H10;
- secondary;
- 35K10;
- 35B40;
- 47D07;
- Mathematics - Analysis of PDEs;
- 35Q84;
- 35H10 (Primary);
- 35K10;
- 35B40;
- 47D07 (Secondary)