“IONKIN SHARTLI BIR O‘LCHAMLI ISSIQLIK TARQALISH INTEGRO-DIFFERENSIAL TENGLAMADAN YADRONI ANIQLASHNING TESKARI MASALASI”

This paper investigates an inverse problem of determining the kernel for a one-dimensional integro-differential heat conduction equation with the Ionkin boundary condition. The problem is significant for reconstructing physical properties of the medium and refining mathematical models of heat transfer processes. The formulation of the inverse problem, issues of well-posedness, and conditions for existence and uniqueness of solutions are analyzed. Taking into account the specific features of the Ionkin condition, an approach based on the theory of integral equations is proposed. The obtained results can be applied in mathematical modeling of heat transfer processes and various engineering applications.