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

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  • The well-posedness of a chemotaxis system with indirect signal production in a two-dimensional domain is shown, all solutions being global unlike for 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.

    Mathematics Subject Classification: Primary: 35B40; Secondary: 35M33, 35K10, 35Q92.

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