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.
| Origine | Fichiers produits par l'(les) auteur(s) |
|---|
Loading...