On the rates of decay to equilibrium in degenerate and defective Fokker–Planck equations

Arnold, Anton; Einav, Amit; Wöhrer, Tobias

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.

Citation

Arnold, A., Einav, A., & Wöhrer, T. (2018). On the rates of decay to equilibrium in degenerate and defective Fokker–Planck equations. Journal of Differential Equations, 264(11), 6843-6872. https://doi.org/10.1016/j.jde.2018.01.052

• Journal Article Type: Article
• Acceptance Date: Sep 30, 2017
• Online Publication Date: Feb 21, 2018
• Publication Date: Mar 16, 2018
• Deposit Date: Nov 16, 2020
• Journal: Journal of Differential Equations
• Print ISSN: 0022-0396
• Electronic ISSN: 1090-2732
• Publisher: Elsevier
• Volume: 264
• Issue: 11
• Pages: 6843-6872
• DOI: https://doi.org/10.1016/j.jde.2018.01.052
• Public URL: https://durham-repository.worktribe.com/output/1257210