On solvability of the inverse problem for the one-dimensional parabolic equation with unknown time-dependent coefficient under integral observation

In this article, we study the inverse problem of determination of time-dependent coefficient in the parabolic equation. We prove existence and uniqueness theorem for the solution of the inverse problem with nonlocal boundary conditions and integral observation. The proof is based on a priori estimates obtained in this article and the results on solvability of corresponding direct problem for the equarion under consideration.