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arXiv · 1810.06909

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

Philippe Laurençot
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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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Philippe Laurençot. 2018-10-16. Global bounded and unbounded solutions to a chemotaxis system with indirect signal production. https://arxiv.org/abs/1810.06909

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