Kinetic Equations with Reflecting Boundary Conditions

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Abstract
A general abstract model of time-independent kinetic equations on the half-line is presented. The existence and uniqueness of the solution is proved under specified incoming flux and nonmultiplying boundary reflection processes. An iterative method is formulated for computing in principle the solution by using the solution of the analogous problem without reflection. In many concrete cases (e.g. neutron transport, BGK model in rarefied gas dynamics, etc.) the available explicit expression for the latter provides the actual solution of the general problem. Possible generalizations and open problems are briefly discussed.

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