Journal of Mathematical Sciences

, Volume 190, Issue 6, pp 848–858 | Cite as

Stationary heat conduction processes in bodies of randomly inhomogeneous structure

  • O. Yu. Chernukha
  • P. R. Pelekh

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.


Body Volume Neumann Series Inhomogeneous Body Stationary Heat Conduction Stochastic Homogenization 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • O. Yu. Chernukha
    • 1
  • P. R. Pelekh
    • 1
  1. 1.Center of Mathematical Modeling, Pidstryhach Institute for Applied Problems of Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

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