We consider the boundary value problem for the radiative transfer equation with conditions of internal diffusive reflection of radiation. Under the assumption that the absorption and scattering coefficients tend to infinity, we study the limit behavior of solutions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. A. Amosov, “The limit connection between two problems of radiation heat transfer,” Soviet. Phys. Dokl. 24, No. 6, 439–441 (1979).
M. T. Laitinen, “Asymptotic analysis of conductive-radiative heat transfer,” Asympt. Anal. 29, 323–342 (2002).
A. Bensoussan, J.-L. Lions, G. C. Papanicolaou, “Boundary Layers and Homogeneization of Transport Processes,” Publ. Res. Inst. Math. Sci., Kyoto Univ. 15, 53–157 (1979).
C. Bardos, R. Santos, and R. Sentis, “Diffusion approximation and computation of the critical size,” Trans. Am. Math. Soc. 284, No. 2, 617–649 (1984).
C. Bardos, F. Golse, B. Perthame, and R. Sentis, “The nonaccretive radiative transfer equations: Existence of solutions and rosseland approximation,” J. Funct. Anal. 77, No. 2, 434–460 (1988).
S. Chandrasekhar, Radiative Transfer, Calderon Press, Oxford (1950).
I. W. Busbridge, The Mathematics of Radiative Transfer, Cambridge Univ. Press, Cambridge (1960).
V. Kourganoff, Basic Methods in Transfer Problems, Dover, New York (1963).
V. V. Sobolev, A Treatise on Radiative Transfer, D. Van Nostrand, Princenton, NJ (1963).
A. A. Amosov, “Radiative transfer equation with Freshnel reflection and refraction conditions in a system of bodies with piecewise smooth boundaries,” J. Math. Sci. 219, No. 6, 821–849 (2016).
A. A. Amosov, Boundary Value Problems for the Radiative Transfer Equation with Reflection and Refraction Conditions [in Russian], Tamara Rozhkovskaya Publisher, Novosibirsk (2017).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Problemy Matematicheskogo Analiza 124, 2023, pp. 15-30.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Amosov, A.A. Limit Behavior of Solutions to the Radiative Transfer Equation as Coefficients of Absorption and Scattering Tend to Infinity. J Math Sci 270, 752–769 (2023). https://doi.org/10.1007/s10958-023-06387-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-023-06387-0