Mon, October 7, 2019
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5:00pm [5:15pm] Jean Dolbeault. : University of Paris IX - Dauphine.
Description:
IITB Mathematics Colloquium via videoconference. Speaker: Jean Dolbeault. Affiliation: University of Paris IX - Dauphine. Date and Time: Monday 07 October, 5:15 pm - 6:15 pm. Venue: Ramanujan Hall, Department of Mathematics. Title: Hypocoercivity. Abstract: The purpose of hypocoercivity is to obtain rates for solutions of non-purely diffusive equations, in asymptotic regimes. This is a very useful technique for kinetic equations. After reviewing some easy results based on hypo-ellipticity, the lecture will focus on linear kinetic equations without regularizing effects and the L2 hypocoercivity method. Some motivations will be introduced, with a toy model. The core of the lecture will be a theoretical result based on a joint work with C. Mouhot and C. Schmeiser. Initially intended for systems with compactness or confinement in position space and simple local equilibira, the method has been extended to various local equilibria in velocities and non-compact situations in positions. It is also flexible enough to include non-local transport terms associated with Poisson coupling. Some recent results rely on various, deep functional inequalities. An application to the linearized Vlasov-Poisson-Fokker-Planck system will also be briefly presented.
6:00pm