On the solution of an inverse problem for a multidimensional parabolic equation

We study the inverse problem for a multidimensional parabolic equation with an unknown coefficient at the differential operator of second order with respect to a chosen variable with the Cauchy data. The initial condition has a special form and is given in the form of the scalar product of two vector-valued functions that depend on different variables. We obtain sufficient conditions for the existence and uniqueness of the solution to an auxiliary direct problem and the initial inverse problem. We use the weak approximation method for the proof.