Global existence of classical solutions is proven for a Keller-Segel system with non-increasing motility in any dimension, with uniform boundedness under superlinear damping and a critical mass threshold for blow-up in 2D with exponential motility.
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On a Keller--Segel System with Density-Suppressed Motility, Indirect Signal Production, and External Sources
Global existence of classical solutions is proven for a Keller-Segel system with non-increasing motility in any dimension, with uniform boundedness under superlinear damping and a critical mass threshold for blow-up in 2D with exponential motility.