One-Dimensional Inverse Problems of Finding the Kernel of Integrodifferential Heat Equation in a Bounded Domain

We consider an integrodifferential heat equation with time-convolution integral on the right-hand side. The direct problem is an initial boundary-value problem for this equation. We consider two inverse problems for this direct problem, namely, the problems of finding the kernel of the integral term for given two additional conditions imposed on the solution of the direct problem. These problems are replaced with equivalent systems of integral equations for the unknown functions, and the unique solvability of the inverse problems is proved by using the principle of contracting mapping,