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Constructive theory of scalar characteristic equations of the theory of radiation transport: I. Basic assertions of the theory and conditions for the applicability of the truncation method

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Abstract

We describe a number of general properties of solutions of the scalar characteristic equations in the radiation transport theory and state constructive necessary and sufficient conditions for the nontrivial solvability of these equations in the framework of assumptions under which they are Fredholm integral equations. The construction of solutions of these integral equations in analytic form can be reduced to finding solutions of infinite tridiagonal systems of linear algebraic equations. We study the analytic properties of solutions of such systems and derive sufficient conditions for the applicability of the truncation method for the construction of their strict solutions.

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Authors and Affiliations

  1. Belarus National Technical University, Minsk, Belarus

    N. N. Rogovtsov

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  1. N. N. Rogovtsov
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Correspondence to N. N. Rogovtsov.

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Original Russian Text © N.N. Rogovtsov, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 2, pp. 263–276.

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Rogovtsov, N.N. Constructive theory of scalar characteristic equations of the theory of radiation transport: I. Basic assertions of the theory and conditions for the applicability of the truncation method. Diff Equat 51, 268–281 (2015). https://doi.org/10.1134/S0012266115020111

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