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Boundedness of the Stationary Solution to the Boltzmann Equation with Spatial Smearing, Diffusive Boundary Conditions, and Lions’ Collision Kernel
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
2018 (English)In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 50, no 6, p. 5761-5782Article in journal (Refereed) Published
Abstract [en]

We investigate the Boltzmann equation with spatial smearing, diffusive boundary conditions, and Lions’ collision kernel. Both the physical as well as the velocity space, are assumed to be bounded. Existence and uniqueness of a stationary solution, which is a probability density, has been demonstrated in [S. Caprino, M. Pulvirenti, and W. Wagner, SIAM J. Math. Anal., 29 (1998), pp. 913–934] under a certain smallness assumption on the collision term. We prove that whenever there is a stationary solution then it is a.e. positively bounded from below and above.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, SIAM , 2018. Vol. 50, no 6, p. 5761-5782
Keywords [en]
Boltzmann equation, stationarity, spatial smearing, diffusive boundary conditions, Lions’ collision kernel
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-153474DOI: 10.1137/17M1160446ISI: 000453786500003OAI: oai:DiVA.org:liu-153474DiVA, id: diva2:1272347
Available from: 2018-12-19 Created: 2018-12-19 Last updated: 2019-03-22Bibliographically approved

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Löbus, Jörg-Uwe

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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Language
  • de-DE
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