On the problem of identification of two lower coefficients and the coefficient by the derivative with respect to time in the parabolic equation

The theorem of existence and uniqueness of classical solution of identification problem of two lower coefficients and the coefficient by the derivative with respect to time in the class of smooth bounded functions is proved.
In the proof of the existence and uniqueness of the inverse problem solution using the overdetermination conditions, the original inverse problem is reduced to the direct problem for the loaded (containing traces of unknown functions and their derivatives) equation. The investigation of the correctness of the direct problem is obtained by the method of weak approximation.