SUPPRESSION OF BLOW UP BY A LOGISTIC SOURCE IN 2D KELLER-SEGEL SYSTEM WITH FRACTIONAL DISSIPATION

Jan Burczak (1) , Rafael Granero-Belinchón (2)

1 PAN - Institut of Mathematics - Polish Academy of Sciences
2 EDPA - Équations aux dérivées partielles, analyse

We consider a two dimensional parabolic-elliptic Keller-Segel equation with a logistic forcing and a fractional diffusion of order α. We obtain existence of global in time regular solution for arbitrary initial data with no size restrictions and c < α ≤ 2, where c ∈ (0, 2) depends on the equation's parameters. For an even wider range of α s, we prove existence of global in time weak solution for general initial data.

Domaines: Equations aux dérivées partielles [math.AP]

Jan Burczak, Rafael Granero-Belinchón. SUPPRESSION OF BLOW UP BY A LOGISTIC SOURCE IN 2D KELLER-SEGEL SYSTEM WITH FRACTIONAL DISSIPATION. 2016. ⟨hal-01366254⟩