"Quantitative Geometric Control in Kinetic Theory"Mouhot, ClémentWe consider a large class of linear kinetic equations combining transport and a linear collision operator on the kinetic variable, where the collision kernel is allowed to vanish on part of the spatial domain. We prove the first quantitative estimates of relaxation to equilibrium (spectral gap) under a geometric control condition similar to that used for wave equations. The proof is based on a novel elementary method based on trajectories and quantitative divergence inequalities, which sheds new light on the initial-boundary-value problem as well. This is a joint work with F. Hérau, H. Hutridurga and H. Dietert. |
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