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.