## Abstract

We consider a non-linear half-space problem related to the condensation problem for the discrete Boltzmann equation and extend some known results for a single-component gas to the case when a non-condensable gas is present. The vapor is assumed to tend to an assigned Maxwellian at infinity, as the non-condensable gas tends to zero at infinity. We assume that the vapor is completely absorbed and that the non-condensable gas is diffusively reflected at the condensed phase and that the vapor molecules leaving the condensed phase are distributed according to a given distribution. The conditions, on the given distribution, needed for the existence of a unique solution of the problem are investigated. We also find exact solvability conditions and solutions for a simplified six+four-velocity model, as the given distribution is a Maxwellian at rest, and study a simplified twelve+six-velocity model.

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## Acknowledgements

This work was initiated during a stay at Kyoto University as JSPS Postdoctoral Fellow, with a grant from the Japan Society for the Promotion of Science (No. PE 09549). The author wants to thank Professor Kazuo Aoki for the nice hospitality and for proposing this work.

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Bernhoff, N. Half-Space Problem for the Discrete Boltzmann Equation: Condensing Vapor Flow in the Presence of a Non-condensable Gas.
*J Stat Phys* **147**, 1156–1181 (2012). https://doi.org/10.1007/s10955-012-0513-y

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DOI: https://doi.org/10.1007/s10955-012-0513-y