Recovering of the heat transfer coefficient in transmission problems with imperfect contact conditions

We consider systems of parabolic equations and well-posedness questions in Sobolev spaces of inverse problems of recovering the heat transfer coefficients at the interface which are included in the transmission condition of the imperfect contact type. Under certain conditions on the data, it is demonstrated that there exists a unique solution to the problem. The proof employs a priori estimates and the fixed-point theorem.