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

Source 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.