LARGE TIME ASYMPTOTIC BEHAVIORS OF TWO TYPES OF FAST DIFFUSION EQUATIONS

Chuqi Cao (1) , Xingyu Li (2)

1 Yau Mathematical Science Center and Beijing Institute of Mathematical Sciences and Applications
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Consider two types of nonlinear fast diffusion equations in R^N. For the external drift case, it is a natural extension of the simple case that the external is harmonic. In this paper we can prove the large time asymptotic behavior to the stationary states by using entropy methods. For the more complicated mead-field type case with the convolution term, we prove that for some special cases, it also exists large time asymptotic behaviour.

Mots clés: nonlinear diffusion; mean field equations; free energy; large time asymptotics; Hardy-Poincaré inequality AMS subject classifications: 35K55; 35B40; 35P15

Domaines: Equations aux dérivées partielles [math.AP]

Chuqi Cao, Xingyu Li. LARGE TIME ASYMPTOTIC BEHAVIORS OF TWO TYPES OF FAST DIFFUSION EQUATIONS. 2020. ⟨hal-02987235v1⟩