The article considers the start control and the nal observation of solutions to the Showalter Sidorov problem for the mathematical model of an I-beam deformation. We construct the sucient conditions for the existence of the start control and the nal observation by weak generalized solutions of the considered model with the initial Showalter Sidorov condition. Based on the theoretical results, we construct the algorithm of the numerical method to solve the problem of start control and nal observation for the model of an I-beam deformation. The results of computational experiments are presented.Keywords: Sobolev type equation; problem of start control and nal observation; model of I-beam deformation; the Galerkin method; decomposition method.

Статья посвящена исследованию задачи Коши для одной математической модели распределения потенциалов в кристаллическом полупроводнике. Под полупроводником мы будем понимать вещества, обладающие конечной электропроводностью, быстро возрастающей с ростом температуры. Математическая модель распределения потенциалов строится на основе полулинейного уравнения соболевского типа, дополненного условиями Дирихле и Коши. Строятся условия существования решения исследуемой модели на основе метода фазового пространства. Приводятся условия продолжимости решения по времени. Ключевые слова: уравнения соболевского типа; математическая модель распределения потенциалов в кристаллическом полупроводнике; метод фазового пространства; квазистационарные полутраектории.

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The article considers the numerical research of the mathematical model of control of potential distribution in a crystalline semiconductor. This model based on the problem of start control and final observation by weak generalized solutions of mathematical model of potential distribution in a crystalline semiconductor. This model belongs to the class of mathematical models based on semilinear Sobolev type equations with p-coercive and s-monotonous operators. We have shown the existence and uniqueness of a weak generalized solution of the investigated model with the initial condition of Showalter-Sidorov and found sufficient conditions the existence of a solution to the problem of start control and final observation. We construct the algorithm of the numerical method to solve the problem of start control and final observation for the model of control potential distribution in a crystalline semiconductor, based on method of decomposition and method of Galerkin. Computational experiments are given.

The paper considers a mathematical model of potentials optimal distribution in a crystalline semiconductor. This model is based on the problem of optimal control of weak generalized solutions of the mathematical model of the potential distribution in a crystalline semiconductor with the Showalter–Sidorov condition. The theoretical results obtained by us earlier made it possible to develop an algorithm for a numerical method for finding an approximate one by solutions of the optimal control problem for the problem under study, based on the methods of decomposition, Ritz, penalty and Galerkin’s projection method. The results of a computational experiment are presented.