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| We prove an inequality between the entropy and the production of entropy for the linear Boltzmann equation $\partial_t f = Q(f,M)$, where $M$ is a Maxwellian. This is an interesting kind of inequality, similar to a log-Sobolev inequality, and in fact we show that in the limit of grazing collisions one can obtain from it the log-Sobolev inequality for a particular Fokker-Planck equation. We show that this inequality is related to other known ones involving the bilinear Boltzmann operator, and give some applications. |
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