Inverse Problems for the Helmholtz Equation on Finding the Right-Hand Side with Nonlocal Integral Observation.

The paper presents formulations of inverse problems for the Helmholtz equation on finding its right-hand side with a Samarskii–Ionkin-type additional integral condition and the justification of their well-posedness in the Hadamard sense in the class of regular solutions. The uniqueness of solutions of the formulated problems is proved on the basis of integral identities. Solutions of the problem are found in explicit form by the methods of separation of variables and integral equations. [ABSTRACT FROM AUTHOR]