Abstract
We show that every steady discrete velocity model of the Boltzmann equation on the real line,ξ i·(d/dx)f i=C i(f), which satisfies anH-theorem and for which allξ i≠0, has solutions on the half-line (0, ∞) which take prescribed non-negativef i(O) ifξ i>0 and approach a certain manifold of Maxwellians asx→∞. Such solutions give the density distribution in a Knudsen boundary layer in the discrete velocity case.
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Cercignani, C., Illner, R., Pulvirenti, M. et al. On nonlinear stationary half-space problems in discrete kinetic theory. J Stat Phys 52, 885–896 (1988). https://doi.org/10.1007/BF01019733
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DOI: https://doi.org/10.1007/BF01019733