Global bounded and unbounded solutions to a chemotaxis system with indirect signal production

2018/10/16 by Laurençot, Philippe · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.06909

Abstract

The well-posedness of a chemotaxis system with indirect signal production in a two-dimensional domain is shown, all solutions being global unlike the classical Keller-Segel chemotaxis system. Nevertheless, there is a threshold value M_c of the mass of the first component which separates two different behaviours: solutions are bounded when the mass is below M_c while there are unbounded solutions starting from initial conditions having a mass exceeding M_c. This result extends to arbitrary two-dimensional domains a previous result of Tao & Winkler (2017) obtained for radially symmetric solutions to a simplified version of the model in a ball and relies on a different approach involving a Liapunov functional.

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• Parabolic-elliptic and indirect-direct simplifications in chemotaxis systems driven by indirect signalling

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