SÉMINAIRE D'ANALYSE NUMÉRIQUE
Année universitaire 2015-2016
Nicolas VAUCHELET (Laboratoire Jacques-Louis Lions,
Université Pierre et Marie Curie)
Aggregation
of bacteria by chemotaxis: mathematical and numerical analysis.
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 modelling 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.
