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

Abstract

In this paper, we study the minimal Keller-Segel model with a logistic source and obtain quantitative and qualitative descriptions of the competition between logistic damping and other ingredient, especially, chemotactic aggregation to guarantee boundedness and convergence. More specifically, we establish how precisely strong a logistic source can prevent blow-up, and then we obtain an explicit relationship between logistic damping and other ingredient, especially, chemotactic aggregation so that convergences are ensured and their respective convergence rates are explicitly calculated out. Known results in the literature are completed and refined. Furthermore, our findings provide clues on how to produce blowup solutions for KS chemotaxis models with logistic sources.

34 pages, a second revised version; detected typos were amended

References in corpus (3)

• New critical exponents in a fully parabolic quasilinear Keller-Segel and applications to volume filling models
• Boundedness in a quasilinear fully parabolic Keller-Segel system with logistic source
• A class of chemotaxis systems with growth source and nonlinear secretion

Cited by in corpus (12)

• Sub-logistic source can prevent blow-up in the 2D minimal Keller-Segel chemotaxis system
• 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
• Chemotaxis effect vs logistic damping on boundedness in the 2-D minimal Keller-Segel model
• A class of chemotaxis systems with growth source and nonlinear secretion
• Global solvability in a two-species chemotaxis system with signal production
• Emergence of lager densities in chemotaxis system with indirect signal production and non-radial symmetry case
• Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source
• Immediate smoothing and global solutions for initial data in $L^1\times W^{1,2}$ in a Keller-Segel system with logistic terms in 2D
• Global solvability and asymptotical behavior in a two-species chemotaxis model with signal absorption
• Boundedness and asymptotically stability to chemotaxis system with competitive kinetics and nonlocal terms
• Negligibility of haptotaxis effect in a chemotaxis-haptotaxis model