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On half-space problems for the weakly non-linear discrete Boltzmann equation
Karlstad University, Faculty of Technology and Science, Department of Mathematics. (Kinetisk teori)
2010 (English)In: Kinetic and Related Models, ISSN 1937-5093, 1937-5077 (online), Vol. 3, no 2, 195-222 p.Article in journal (Refereed) Published
Abstract [en]

Existence of solutions of weakly non-linear half-space problems for the general discrete velocity (with arbitrarily finite number of velocities) model of the Boltzmann equation are studied. The solutions are assumed to tend to an assigned Maxwellian at infinity, and the data for the outgoing particles at the boundary are assigned, possibly linearly depending on the data for the incoming particles. The conditions, on the data at the boundary, needed for the existence of a unique (in a neighborhood of the assigned Maxwellian) solution of the problem are investigated. In the non-degenerate case (corresponding, in the continuous case, to the case when the Mach number at infinity is different of -1, 0 and 1) implicit conditions are found. Furthermore, under certain assumptions explicit conditions are found, both in the non-degenerate and degenerate cases. Applications to axially symmetric models are studied in more detail

Place, publisher, year, edition, pages
Springfield, MO: American Institute of Mathematical Sciences, 2010. Vol. 3, no 2, 195-222 p.
Keyword [en]
Boltzmann equation, discrete velocity models, half-space problem, boundary layers
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-9680DOI: 10.3934/krm.2010.3.195OAI: oai:DiVA.org:kau-9680DiVA: diva2:493181
Available from: 2012-02-08 Created: 2012-02-08 Last updated: 2013-02-12Bibliographically approved

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