Numerical research for the start control and final observation problem in model of the distribution of potentials in a crystalline semiconductor

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.