Sub-logistic source can prevent blow-up in the 2D minimal Keller-Segel chemotaxis system

摘要

It is well-known that the Neumann initial-boundary value problem for theminimal-chemotaxis-logistic system in a 2D bounded smooth domain has no blow-upfor any choice of parameters. Here, for a large class of kinetic termsincluding sub-logistic sources, we show that the corresponding 2D Neumanninitial-boundary value problems do not possess any blow-up. This illustrates anew phenomenon that even a class of sub-logistic sources can prevent blow-upfor the 2D problem, indicating that logistic damping is not the weakest dampingto guarantee uniform-in-time boundedness for the 2D minimal Keller-Segelchemotaxis model.