MATHEMATICAL MODELING OF HEAT-CONDUCTION PROCESSES IN RANDOMLY INHOMOGENEOUS BODIES USING FEYNMAN DIAGRAMS

摘要

This work is devoted to the mathematical modeling of heat-conduction processes in multiphase bodies with randomly inhomogeneous structure. A nonstationary initial boundary-value problem is formulated on the basis of the Fourier law for a whole body. The technique of Feynman diagrams is applied to the investigation of averaged temperature fields. We obtain the Dyson equation and a nonlocal heat-conduction equation for the temperature field averaged over an ensemble of phase configurations in multiphase randomly inhomogeneous bodies.