Existence, Uniqueness, and Convergence of the Solutions of Models in Kinetic Theory

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Abstract
A recently proved theorem of existence and uniqueness for the linearized Boltzmann equation is extended to two‐ and three‐dimensional domains and general boundary conditions. The proof is valid for collision operators having a finite collision frequency, which can arise either from an angular or a radial cutoff or by assuming a model equation. Finally, convergence of the solutions of kinetic models to solutions of the actual Boltzmann equation is shown to hold for the boundary‐value problems considered in this paper.

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