On some classes of inverse problems of recovering the heat transfer coefficient in stratified media

We consider the well-posedness, in Sobolev spaces, of the inverse problem of recovering the heat transfer coefficient at the interface in the transmission condition of the imperfect contact type. The existence and uniqueness theorem are exhibited. The method is constructive and the approach allows us to develop some numerical methods for solving the problem. The proof relies on a priori estimates and the fixed-point theorem.