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On The Rates of Decay to Equilibrium in Degenerate and Defective Fokker-Planck Equations (1709.10216v2)
Published 29 Sep 2017 in math.AP
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.