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An asymptotic preserving scheme for a kinetic equation describing propagation phenomena

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

The run-and-tumble motion of bacteria such as E. Coli can be represented by a kinetic equation considered with an hyperbolic scaling, and a Hopf-Cole transformation that makes the problem become non-linear. It has been proved that the asymptotic model is a Hamilton-Jacobi equation, in which the Hamiltonian is implicitely defined. Stiff terms appear in the kinetic equation when getting close to the asymptotic. From a numerical point of view, it may make the resolution of the equation hard, unless an appropriate strategy is used. Asymptotic Preserving (AP) schemes are designed to deal with these difficulties, since they are stable along the transition from the mesoscopic to the macroscopic scale. I will present an AP scheme for this nonlinear kinetic equation, which is based on a formal asymptotic analysis of the problem, and on a adaptation of an AP strategy designed for a linear kinetic equation.

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

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