The Kinetic Transport Equation in the Case of Compton Scattering |
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Authors: | D. S. Anikonov D. S. Konovalova |
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Affiliation: | (1) Institute of Applied Mathematics of the Far East Division of the Russian Academy of Sciences, Russia |
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Abstract: | We improve the well-known form of the transport equation accounting for Compton scattering. We pose and study the direct problem of finding the radiation density distribution for given characteristics of a medium and known density of exterior sources. We prove existence and uniqueness theorems for a solution to the boundary value problem under consideration. The character of constraints corresponds mostly to the process of photon migration in a substance whose characteristics vary continuously with the space and energy variables. Unlike similar results, the assertions are proven without using the traditional inequalities for the coefficients of the transport equation. |
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Keywords: | Compton scattering kinetic equation transport theory photon migration |
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