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Instantaneous filling of the vacuum for the Boltzmann equation

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Imagine a box divided into two compartments thanks to a wall, one compartment being empty and the other one containing gas. What would happen if you take the wall out? A mathematical answer to that is the fact that immediately the gas will fill the entire box. In this talk we derive this result for the full Boltzmann equation in the torus and $C^2$ bounded domains in general, and also give an explicit exponential lower bound for the solution.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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