Mathematical Notes

, Volume 105, Issue 1–2, pp 80–90 | Cite as

The Cauchy Problem for the Radiation Transfer Equation with Fresnel and Lambert Matching Conditions

  • I. V. ProkhorovEmail author


The well-posedness of the initial boundary-value problem for the nonstationary radiation transfer equation in a three-dimensional bounded domain with generalized matching conditions at the interfaces is studied. The case of the matching operator expressed as a linear combination of operators of Fresnel and Lambert types is considered. The existence of a unique strongly continuous semigroup of solving operators of the Cauchy problem is proved, and stabilization conditions for the nonstationary solution are obtained.


radiation transfer equation initial boundary-value problem matching conditions Fresnel’s and Lambert’s laws 


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Institute for Applied Mathematics, Far-Eastern BranchRussian Academy of SciencesVladivostokRussia
  2. 2.Far-Eastern Federal UniversityVladivostokRussia

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