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Existence of a solution of an initial-boundary value difference problem for a linear heat equation with a nonlinear boundary condition

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Abstract

A problem of heat propagation in the ground from a heated pipeline with a partially heat-insulating shell is considered. The possibility is proved to construct a numerical solution of a linear heat equation by using a direct finite-difference method in the case when the thermal radiation on the ground surface is taken into account. On the basis of the theorem about the solvability of a system of linear difference equations by means of the sweep method, the existence and uniqueness of a solution of a corresponding difference problem with nonlinear boundary condition are proved.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620219, Russia

    N. A. Vaganova

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  1. N. A. Vaganova
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Correspondence to N. A. Vaganova.

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Original Russian Text © N.A. Vaganova, 2008, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2008, Vol. 14, No. 1.

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Vaganova, N.A. Existence of a solution of an initial-boundary value difference problem for a linear heat equation with a nonlinear boundary condition. Proc. Steklov Inst. Math. 261 (Suppl 1), 260–271 (2008). https://doi.org/10.1134/S0081543808050209

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  • DOI: https://doi.org/10.1134/S0081543808050209

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