This work is devoted to the mathematical modeling of stationary heat conduction processes in randomly inhomogeneous multiphase structures. An integro-differential equation with a random kernel, whose solution is constructed in the form of a Neumann series, is put in correspondence with the boundary-value problem of heat conduction. We establish the conditions of absolute and uniform convergence of this series, in particular, the condition of boundedness of the body volume. It is shown that, for unbounded bodies, the condition of boundedness of the domain occupied by inclusions is necessary for convergence of the Neumann series.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 55, No. 1, pp. 179–187, January–March, 2012.
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Chernukha, O.Y., Pelekh, P.R. Stationary heat conduction processes in bodies of randomly inhomogeneous structure. J Math Sci 190, 848–858 (2013). https://doi.org/10.1007/s10958-013-1293-x
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DOI: https://doi.org/10.1007/s10958-013-1293-x