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

Abstract

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