Journal of Mathematical Sciences, Vol. 270, No. 6, March, 2023 LIMIT BEHAVIOR OF SOLUTIONS TO THE RADIATIVE TRANSFER EQUATION AS COEFFICIENTS OF ABSORPTION AND SCATTERING TEND TO INFINITY A. A. Amosov National Research University “Moscow Power Engineering Institute” 14, Krasnokazarmennaya St., Moscow 111250, Russia AmosovAA@mpei.ru UDC 517.9 We consider the boundary value problem for the radiative transfer equation with condi- tions of internal diffusive reflection of radiation. Under the assumption that the absorp- tion and scattering coefficients tend to infinity, we study the limit behavior of solutions. Bibliography: 11 titles. 1 Introduction When studying complex heat transfer from the mathematical point of view, it is of interest to find out the limit connection between the solutions to the problem of radiative-conductive heat transfer in semitransparent materials with large absorption and scattering coefficients and the solutions to the corresponding problems in opaque materials. This topic is important because, in practice, it is assumed that semitransparent materials with a large absorption coefficient can be considered as opaque and the energy radiation and absorption occur only on the boundaries. This assumption was confirmed by the mathematical results [1], [2] in the case where the radiation scattering is negligible in comparison with absorption or it is absent at all. The propagation of the monochromatic radiation in a semitransparent body G is described by the radiative transfer integro-differential equations ω ·∇I + βI = sS (I )+ κk 2 F, (ω,x) ∈ D. (1.1) The sought function I (ω,x) is defined on the set D =Ω × G, where Ω = {ω ∈ R 3 ||ω| =1}, and is the intensity at x ∈ G of radiation propagating in the direction ω ∈ Ω. In Equation (1.1), ω ·∇I = 3 ∑ i=1 ω i ∂ ∂x i I is the derivative of I along a direction ω. Here, S Translated from Problemy Matematicheskogo Analiza 124, 2023, pp. 15-30. 1072-3374/23/2706-0752 c  2023 Springer Nature Switzerland AG 752 DOI 10.1007/s10958-023-06387-0