Abstract
We study existence and uniqueness results for the one-dimensional Boltzmann equation with inflow and diffusive boundary conditions. Our focus, partly encompasses some of the properties of the Boltzmann collision gain term which play a significant role in existence and uniqueness results. A series of estimates are proven on the collision term which is shown to produce a suitable function space in which the contraction mapping arguments are available.
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This work was done as part of the author’s M.Sc. studies at the University of Victoria.
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Ghomeshi, S. Existence and Uniqueness of Solutions for the Couette Problem. J Stat Phys 118, 265–300 (2005). https://doi.org/10.1007/s10955-004-8784-6
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DOI: https://doi.org/10.1007/s10955-004-8784-6