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Stationary problem of Boltzmann equation. (English) Zbl 1185.35002

Chipot, Michel (ed.), Handbook of differential equations: Stationary partial differential equations. Vol. V. Amsterdam: Elsevier/North Holland (ISBN 978-0-444-53217-6/hbk). Handbook of Differential Equations, 371-485 (2008).
The survey paper is devoted to the stationary problems for the Boltzmann equation. The main attention is paid to the physical situation which led to so called Maxwellian solutions.
The paper contains a wide historical overview and a description of recent results in the area. The main part of the mathematical presentation is divided into three sections, namely, “Half-space problem - nonlinear boundary layer”, “Exterior problem - flow past an obstacle”, and “Time-periodic solution”.
An extended references list is given.
For the entire collection see [Zbl 1173.35001].

MSC:

35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
35Q20 Boltzmann equations
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