A three-dimensional mathematical model and simulation of the impurity diffusion process are developed under the given statistical characteristics of the system of internal stochastically disposed point sources of mass. These sources, possessing varying intensities, are located within the sub-strip according to a uniform distribution. The random source statistics are known, and the problem solution is expressed as the sum of the solution to the homogeneous problem and the convolution of Green’s function with the random point source system. The impurity concentration is averaged. Diffusive fluxes and the total amount of substance passing through any cross-sectional area over a specified time period are modeled using Fick’s laws. General and calculating formulas for averaged diffusive fluxes, including those applicable to steady-state regimes, are derived. A calculating formula for the total substance that has passed through the strip within a given time interval is obtained. A comprehensive software suite is developed to simulate the behavior of the averaged characteristics of the diffusion process influenced by the point source system. The second statistical moments of the impurity concentration are obtained and studied.

Modeling of impurity diffusion processes in a multiphase randomly inhomogeneous body is performed using the Feynman diagram technique. The impurity diffusion equations are formulated for each of the phases separately. Their random boundaries are subject to non-ideal contact conditions for concentration. The contact mass transfer problem is reduced to a partial differential equation describing diffusion in the body as a whole, which accounts for jump discontinuities in the searched function as well as in its derivative at the stochastic interfaces. The obtained problem is transformed into an integro-differential equation involving a random kernel, whose solution is constructed as a Neumann series. Averaging over the ensemble of phase configurations is performed. The Feynman diagram technique is developed to investigate the processes described by parabolic partial differential equations. The mass operator kernel is constructed as a sum of strongly connected diagrams. An integro-differential Dyson equation is obtained for the concentration field. In the Bourret approximation, the Dyson equation is specified for a multiphase randomly inhomogeneous medium with uniform phase distribution. The problem solution, obtained using Feynman diagrams, is compared with the solutions of diffusion problems for a homogeneous layer, one having the coefficients of the base phase and the other having the characteristics averaged over the body volume.

We develop a new mathematical framework for describing impurity diffusion in multiphase, stochastically inhomogeneous media with internal deterministic mass sources. The main contribution of the paper is the structural preservation of the original multiphase problem while reducing it to a single integro-differential diffusion equation for the entire body. Using a Feynman diagram technique, we obtain a Dyson-type equation for the averaged concentration field; its kernel (mass operator) summarizes the cumulative effect of random phase interfaces and internal sources. This diagrammatic formulation offers clear advantages: it systematically organizes the contributions of complex interphase interactions and source terms, ensures convergence of the Neumann-series solution, and facilitates extensions to more intricate source distributions. The approach allows us to analyze the behavior of the averaged impurity concentration under various temporally or spatially distributed internal sources and provides a foundation for further refinement of transport models in complex multiphase systems.

Робота присвячена моделюванню дифу­зійних процесів у шарі за дії випадково розташованого точкового джерела. Досліджені варіанти розташуван­ня джерела за рівномірним і трикутним розподілом на певному проміжку, а також два часткові випадки бе­та-розподілу, які відповідають найімовірнішому зна­ходженню точкового джерела маси в околі верхньої або нижньої границі шару.