On the problem of the identification of some multy-dimensional parabolic equation coefficients in the case of non-homogeneous overdetermination conditions

In this article we consider a problem of determining three unknown highest coefficients of many-dimensional parabolic equation for Cauchy data.
We prove the theorems of existence and uniqueness of solution in the small for the classical inverse problem.
To prove the existence solvability of problem, we will use the method of week approximation.