Very slow stabilization for a nonlinear Fokker–Planck equation. (June 2016)

• Record Type: Journal Article
• Authors: Fila, Marek; Stuke, Hannes
• Is Part Of: Nonlinear analysis. Volume 138(2016)
• Page Start: 93
• Page End: 110
• Publication Date: 2016-06
• Subjects: Fast diffusion equation -- Nonlinear Fokker–Planck equation -- Rate of convergence to steady states; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.01.007
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the asymptotic behaviour near extinction of positive solutions of the fast diffusion equation with critical and subcritical exponents. By a suitable rescaling, the equation is transformed to a nonlinear Fokker–Planck equation. We show that the rate of convergence to regular and singular steady states of the transformed equation can be arbitrarily slow for suitable initial data. Our results reveal the difference in the slow rates occurring in the critical and the subcritical case and they yield a new class of extinction rates for the fast diffusion equation.