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The boundary-value problem for the transport equation with purely Compton scattering

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Abstract

We study the boundary-value problem of finding the distribution density or the intensity of photon flows in an arbitrary medium. The main ingredient of the mathematical model is the stationary transport equation. The radiation characteristics of the medium and sources of radiation are assumed known; i.e., the problem under consideration is a classical direct problem of mathematical physics. The article is a continuation of the previous article by the authors. We have managed to extend essentially the classes of functions describing the process of photon migration so as to cover the resonance phenomena and cases of compound media. The result of the article is a unique existence theorem concerning the boundary-value problem for the transport equation.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    D. S. Anikonov & D. S. Konovalova

Authors
  1. D. S. Anikonov
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  2. D. S. Konovalova
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Additional information

Original Russian Text Copyright © 2005 Anikonov D. S. and Konovalova D. S.

The authors were supported by the Russian Foundation for Basic Research (Grant 04-01-00126) and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-1172.2003.1).

Translated from Sibirski\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath} \) Matematicheski\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath} \) Zhurnal, Vol. 46, No. 1, pp. 3–16, January–February, 2005.

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Anikonov, D.S., Konovalova, D.S. The boundary-value problem for the transport equation with purely Compton scattering. Sib Math J 46, 1–12 (2005). https://doi.org/10.1007/s11202-005-0001-6

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  • DOI: https://doi.org/10.1007/s11202-005-0001-6

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