Summary
The Boltzmann equation for a dilute spatially homogeneous gas —wherein the scattering is isotropic—is considered. It is shown that the equation can be projected into a Hilbert space, resulting in an autonomous differential system which, from a computational point of view, is very appealing. Conservation laws are automatically obeyed; and, for models with isotropic cross-sections depending on the energy with a power law, the requisite matrix elements can be analytically evaluated as finite sums of products of gamma-functions.
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Barnsley, M.F., Turchetti, G. Projection method for Boltzmann energy equations. Lett. Nuovo Cimento 33, 347–351 (1982). https://doi.org/10.1007/BF02725561
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DOI: https://doi.org/10.1007/BF02725561