Siberian Federal University

In this paper we study the solvability of inverse problems for an elliptic equation of the form utt + uxx + μ(t)u = f (x, t) + q(t)h(x, t), where the coefficient q(t) is unknown. The existence and uniqueness theorems of the regular solutions are proved. The investigation methods are based on the transition from the original inverse problem to a nonlocal problem with conditions of the type of Samarski–Ionkin conditions. Keywords: elliptic equation, unknown coefficient, boundary condition, existence, uniqueness of solution, Samarski–Ionkin conditions