Abstract
We study a collisionless kinetic equation describing density distribution function of the position and velocity of particles moving in a slab with finite thickness and with a partly diffusive boundary reflection. In particular, we deal with existence of an invariant density and with the convergence to the equilibrium. We also study the long time behavior of densities when the equilibrium does not exists.
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This paper was partially supported by the Polish National Science Centre Grant No. 2014/13/B/ST1/00224 (RR). This work was written while R.R. was a visitor to Université de Franche-Comté and the authors thank Université de Franche-Comté for financial support of this visit.
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Mokhtar-Kharroubi, M., Rudnicki, R. On Asymptotic Stability and Sweeping of Collisionless Kinetic Equations. Acta Appl Math 147, 19–38 (2017). https://doi.org/10.1007/s10440-016-0066-1
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DOI: https://doi.org/10.1007/s10440-016-0066-1