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math.AP2018
Blowing up radial solutions in the minimal Keller-Segel model of chemotaxis
Piotr Biler, Jacek Zienkiewicz
We consider the simplest parabolic-elliptic model of chemotaxis in the whole space in several dimensions. Criteria for the blowup of radially symmetric solutions in terms of suitab…
math.AP2017
Large global-in-time solutions to a nonlocal model of chemotaxis
Piotr Biler, Grzegorz Karch, Jacek Zienkiewicz
We consider the parabolic-elliptic model for the chemotaxis with fractional (anomalous) diffusion. Global-in-time solutions are constructed under (nearly) optimal assumptions on th…