On some classes of coefficient inverse problems of recovering thermophysical parameters in stratified media

We examine the question of regular solvability in Sobolev spaces of parabolic inverse coefficient problems in stratified media with conjugation conditions of the diffraction type. A solution has all generalized the derivatives occurring in the equation summable with some power. The over determination conditions are the values of the solution at some collection of points lying inside the domain. The proof is based on a priori estimates and the fixed point theorem.