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Boundary layers for discrete kinetic models: Multicomponent mixtures, polyatomic molecules, bimolecular reactions, and quantum kinetic equations
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). (Kinetisk teori)ORCID iD: 0000-0003-1232-3272
2017 (English)In: Kinetic and Related Models, ISSN 1937-5093, E-ISSN 1937-5077, Vol. 10, no 4, p. 925-955Article in journal (Refereed) Published
Abstract [en]

We consider some extensions of the classical discrete Boltzmann equation to the cases of multicomponent mixtures, polyatomic molecules (with a finite number of different internal energies), and chemical reactions, but also general discrete quantum kinetic Boltzmann-like equations; discrete versions of the Nordheim-Boltzmann (or Uehling-Uhlenbeck) equation for bosons and fermions and a kinetic equation for excitations in a Bose gas interacting witha Bose-Einstein condensate. In each case we have an H-theorem and so for the planar stationary half-space problem, we have convergence to an equilibrium distribution at infinity (or at least a manifold of equilibrium distributions). In particular, we consider the nonlinear half-space problem of condensation and evaporation for these discrete Boltzmann-like equations. We assume that the flow tends to a stationary point at infinity and that the outgoing flow is known at the wall, maybe also partly linearly depending on the incoming flow. We find that the systems we obtain are of similar structures as for the classical discrete Boltzmann equation (for single species), and that previously obtained results for the discrete Boltzmann equation can be applied after being generalized. Then the number of conditions on the assigned data at the wall needed for existence of a unique solution is found. The number of parameters to be specified in the boundary conditions depends on if we have subsonic or supersonic condensation or evaporation. All our results are valid for any finite number of velocities.

Place, publisher, year, edition, pages
American Institute of Mathematical Sciences, 2017. Vol. 10, no 4, p. 925-955
Keywords [en]
Nordheim-Boltzmann equation, discrete velocity models, Boltzmann equation, mixtures, polyatomic molecules, chemical reactions, boundary layers, half-space problems
National Category
Other Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-48057DOI: 10.3934/krm.2017037ISI: 000396010800003OAI: oai:DiVA.org:kau-48057DiVA, id: diva2:1078190
Available from: 2017-03-02 Created: 2017-03-02 Last updated: 2018-12-17Bibliographically approved

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Bernhoff, Niclas

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