Mathematical Modeling of the Processes of Thermodiffusion of the Decaying Substance in a Stochastically Inhomogeneous Layered Strip

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We study the processes of thermodiffusion with regard for the decay of a substance in a two-phase randomly inhomogeneous layered strip. The statement of a contact-boundary-value problem is formulated on the basis of the theory of binary systems with conditions of perfect contact for temperature and imperfect conditions for concentration. The system of equations of thermodiffusion of decaying particles is obtained for the entire body. The system of integrodifferential equations equivalent to the source contact boundary-value problem is formulated. Its solution is constructed by the method of successive approximations. The random fields of temperature and concentration of decaying particles are found in the form of Neumann series. The conditions of absolute and uniform convergence of the series are established. The procedure of averaging of the random fields is carried out over the ensemble of phase configurations with uniform distribution function.