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Convergence to equilibrium for degenerate kinetic equations

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If you have a question about this talk, please contact Prof. Clément Mouhot .

We study the decay to the equilibrium state for the solution of the linear Boltzmann equation in the torus, by allowing that the non-negative cross section can vanish in a subregion X of the domain, with positive Lebesgue measure. We give a counterexample which shows that the asymptotic rate of convergence to equilibrium cannot be better than t^{-1/2} in the general case and identify the necessary and sufficient condition on X that guarantees the exponential decay to equilibrium.

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

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