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

Abstract

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

submitted

References in corpus (1)

• How strong a logistic damping can prevent blow-up for the minimal Keller-Segel chemotaxis system?

Cited by in corpus (4)

• Finite-time blow-up in a two-dimensional Keller--Segel system with an environmental dependent logistic source
• Approaching optimality in blow-up results for Keller-Segel systems with logistic-type dampening
• A new result for 2D boundedness of solutions to a chemotaxis--haptotaxis model with/without sub-logistic source
• Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic-elliptic Keller-Segel systems