On nonlinear stationary half-space problems in discrete kinetic theory |
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Authors: | Carlo Cercignani Reinhard Illner Mario Pulvirenti Marvin Shinbrot |
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Institution: | (1) Politecnico di Milano, 20133 Milan, Italy;(2) University of Victoria, V8W 2Y2 Victoria, British Columbia, Canada;(3) Universita de l'Aquila, l'Aquila, Italy |
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Abstract: | We show that every steady discrete velocity model of the Boltzmann equation on the real line,
i·(d/dx)f
i=C
i(f), which satisfies anH-theorem and for which all
i0, has solutions on the half-line (0, ) which take prescribed non-negativef
i(O) if
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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Keywords: | Boltzmann equation steady discrete velocity models half-space problem |
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