One-dimensional inverse problems of finding the kernel of the integro-differential heat equation in a bounded domain - Durdiev, D. K.; Zhumaev , Zh. Zh. (Ukrains’kyi Matematychnyi Zhurnal, 2021)
UDC 517.958We consider the integro-differential heat equation with a time convolution integral on the right-hand side. The direct problem is an initial-boundary problem for the integro–differential equation. We study two inverse problems for this direct problem, which consist in finding the kernel of the integral term provided that two additional conditions on the solution of the direct problem are given. These problems are replaced with equivalent systems of integral equations with respect to unknown functions and, using the contraction mapping principle, we prove the unique solvability of the inverse problems.