Inverse Problems of Finding a Source in the Heat Equation from a Nonlocal Observation

The article presents the statement of inverse problems of finding the right-hand side of theheat equation from an additional integral condition and justifies their Hadamard well-posedness inthe class of regular solutions. The uniqueness of solutions of the problems is proved on the basis ofintegral identities. The solutions of the problems are constructed explicitly using separation ofvariables and the integral equation method.