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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Arnold, Anton¹  Einav, Amit¹  Woehrer, Tobias¹ 

[1] Vienna Univ Technol, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

关键词: Fokker-Planck equations;    Spectral theory;    Non-symmetric hypercontractivity;    Long time behaviour;   

DOI  :  10.1016/j.jde.2018.01.052

来源: Elsevier

【 摘 要 】

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. (C) 2018 The Authors. Published by Elsevier Inc.

【 授权许可】

Free