, Volume 62, Issue 3, pp 387–401 | Cite as

Analytic Solution of the Nonlinear Radiative Diffusion Problem in a One-Dimensional Purely Scattering Medium. I

  • H. V. PikichyanEmail author

A simple example of a nonlinear problem of reflection and transmission of radiation by a one-dimensional scattering and absorbing isotropic medium of finite geometric thickness with conservative and isotropic scattering is examined. The effectiveness of the linear images (LI) method developed previously by the author for solving nonlinear radiative transfer problems is demonstrated. An explicit expression is obtained for the desired LI. It is used to obtain a solution of the reflection and transmission problem for two-sided illumination of a medium of finite thickness in explicit closed form and the radiation field inside it is determined for two mutually opposite statements of the problem: “direct” and “inverse.” Numerical results are given illustrating the difference between the solutions of these problems in the linear and nonlinear cases.


radiative transfer nonlinear problem 


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Authors and Affiliations

  1. 1.V. A. Ambartsumyan Byurakan Astrophysical ObservatoryByurakanArmenia

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