Rates of Convergence to Non-degenerate Asymptotic Profiles for Fast Diffusion via Energy Methods

• DOI: 10.1007/s00205-023-01843-2
• Publication Date: 2023-03-26T21:50:55Z
• Authors: Goro Akagi
• Keywords: Primary: 35K67, Secondary: 35B40, 35B35; Mathematics - Analysis of PDEs; 0103 physical sciences; FOS: Mathematics; FOS: Physical sciences; Mathematical Physics (math-ph); 0101 mathematics; 01 natural sciences; Mathematical Physics; Analysis of PDEs (math.AP)

Abstract This paper is concerned with a quantitative analysis of asymptotic behaviors (possibly sign-changing) solutions to the Cauchy–Dirichlet problem for fast diffusion equation posed on bounded domains Sobolev subcritical exponents. More precisely, rates convergence non-degenerate profiles are revealed via an energy method. The sharp rate positive ones was recently discussed by Bonforte and Figalli (Commun Pure Appl Math 74:744-789, 2021) based entropy An alternative proof their result also provided. Furthermore, dynamics flows changing signs more specifically under concrete settings; in particular, exponential stability some sign-changing proved dumbbell initial data certain symmetry.