Large Time Asymptotic Behaviors of Two Types of Fast Diffusion Equations
Cao, Chuqi; Li, Xingyu (2021), Large Time Asymptotic Behaviors of Two Types of Fast Diffusion Equations. https://basepub.dauphine.psl.eu/handle/123456789/22373
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-02987235
Series titleCahier de recherche du CEREMADE
MetadataShow full item record
Yau Mathematical Science Center and Beijing Institute of Mathematical Sciences and Applications
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We consider two types of non linear fast diffusion equations in R^N: (1) External drift type equation with general external potential. It is a natural extension of the harmonic potential case, which has been studied in many papers. In this paper we can prove the large time asymptotic behavior to the stationary state by using entropy methods. (2) Mean-field type equation with the convolution term. The stationary solution is the min- imizer of the free energy functional, which has direct relation with reverse Hardy-Littlewood- Sobolev inequalities. In this paper, we prove that for some special cases, it also exists large time asymptotic behavior to the stationary state.
Subjects / Keywordsnonlinear diffusion; mean field equations; free energy; large time asymptotics; Hardy-Poincaré inequality; nonlinear fast diffusion; Fisher information: large time asymptotic; reverse Hardy-Littlewood-Sobolev inequality
Showing items related by title and author.
L2-Hypocoercivity and large time asymptotics of the linearized Vlasov-Poisson-Fokker-Planck system Addala, Lanoir; Dolbeault, Jean; Li, Xingyu; Lazhar Tayeb, Mohamed (2021) Article accepté pour publication ou publié