Aggregation of bacteria by chemotaxis: mathematical and numerical analysis

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• Nicolas Vauchelet (Univ. Paris 13)
• Thursday 24 November 2016, 14:00-15:00
• CMS, MR5.

If you have a question about this talk, please contact Ariane Trescases.

Chemotaxis is the phenomenon by which cells direct their motion according to a chemical present in their environment. In the case of positive chemotaxis, strong aggregation may occur that create patch. From a mathematical point of view, it leads to the study of the so-called aggregation equation which describes the interaction through a potential. Such model can be derived thanks to a hyperbolic limit of kinetic equations modeling the run-and-tumble process of bacteria. In this case the interacting potential is pointy, then solutions of aggregation equation may blow-up in finite time. In this work, we propose to study the existence of weak measure solutions for such aggregation equation, which allows to define solutions beyond the blow-up time. Our approach is based on the definition of weak measure solutions for transport equation with discontinuous coefficients. Then we investigate its numerical simulations and propose a numerical analysis.

This talk is part of the Partial Differential Equations seminar series.

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