Modeling of potential fields in media with a thin inclusion by the method of deforming operators

Background. Modeling of potential fields in media with a thin inclusion is carried out by the method of deforming operators. The topicality of the method lies in its capacity to significantly simplify the calculations; it opens new possibilities of research of the models of potential fields. The study is aimed at analytical description of potential fields in media with a thin inclusion and research of media with plane and central symmetry. Materials and methods. Modeling of potential fields in media with a thin inclusion is carried out using the method of deforming operators. Results. The authors revealed the analytical description of potential fields in sectionally-homogeneous media. The researchers obtained the expressions of a deforming operator that converts a homogeneous Dirichlet problem into a sectionally-homogeneous. The article reveals the discovered asymptotic expressions of a deforming operator, based on the Euler-Maclaurin summation formula. The authors investigated potential fields for the case of media with plane and central symmetry. The researchers determined the physical sense of a deforming operator of transformation, when the thermal capacity coefficients of layers significantly differ: solution component with accuracy up to a numerical factor approximately equals to the solution of the third homogeneous boundary problem. Conclusions. The study revealed the possibility of distribution of the deforming operators method application results in order to create analytical models of two-layer potential fields in multilayer plates.