Today, the next General Institute seminar was held at the Institute of Mathematics and Mechanics of the Ministry of Science and Education of the Republic of Azerbaijan. Elvin Ibrahim oglu Azizbeyov, Ph.D. of the General Institute, gave a report on “Determination of the right-hand side and time-dependent coefficients in the two-dimensional parabolic equation at the same time.”

  In the report, information was provided about inverse problems, their classification, fields of application, and the current state of scientific-research works conducted in this field in recent years, and the existence and uniqueness of the classical solution of the non-local conditional inverse boundary value problem for the two-dimensional parabolic equation was shown. For this purpose, the first considered problem is reduced to an auxiliary problem within certain data and the equivalence of the auxiliary problem to the set problem is proved.

  Then, with the help of the Fourier method, the auxiliary problem is presented in the form of a system of integral equations, and the existence and uniqueness of the solution of the obtained system of integral equations for a small moment of time is proved. Then, some numerical solutions are constructed by discretizing the considered equation and boundary conditions, numerical solutions are given in tabular form for sample examples, and corresponding graphs are shown using MatLab mathematical software package.

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