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Pré-Publication, Document De Travail Année : 2012

On the exponential decay to equilibrium of the degenerate linear Boltzmann equation

Résumé

In this paper we study the decay to the equilibrium state for the solution of the linear Boltzmann equation in the torus $\T^d=\bR^d/\bZ^{d}$, $d \in \N$, by allowing that the non-negative cross section $\sigma$ can vanish in a subregion $X:=\{ x \in \T^d\, \vert \, \sigma(x)=0\}$ of the domain with $\text{meas}(X)\geq 0$ with respect to the Lebesgue measure. We show that the geometrical characterization of $X$ is the key property to produce exponential decay to equilibrium.
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Dates et versions

hal-00724613 , version 1 (22-08-2012)

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  • HAL Id : hal-00724613 , version 1

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Etienne Bernard, Francesco Salvarani. On the exponential decay to equilibrium of the degenerate linear Boltzmann equation. 2012. ⟨hal-00724613⟩
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