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Hypocoercivity for some linear kinetic equations with a boundary

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If you have a question about this talk, please contact Jonathan Ben-Artzi.

We consider the Fokker-Planck equation or the linear Boltzmann equation in a bounded domain with a possible external potential and with specular reflexion conditions at the boundary. We show existence and uniqueness of a weak solution in weighted adapted spaces, and prove explicit exponential time decay to the equilibrium. Hypocoercivity estimates are a consequence of coercivity of the collision part, coercivity in space variable of a Witten Laplacian, and an explicit “cross operator” mixing velocity and space variables. This is a joint work with D. Le Peutrec (Paris 11).

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

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