On determining the coefficient of heat exchange in stratified medium

In the article we consider the well-posedness in Sobolev spaces of the inverse problems of determining the heat exchange coefficient at the interface which is included in the transmission condition of the imperfect contact type. In a cylindrical spatial domain, a second-order parabolic equation is considered. The domain is divided into two sub-domains, on the common part of the boundary of which the transmission condition is set. The heat exchange coefficient included in the transmission condition is sought as end segment in series with time-dependent unknown Fourier coefficients. The equation is supplemented with general boundary conditions and initial conditions, as well as overdetermination conditions. The ovedetermination conditions are the values of a solution at some points lying in the spatial domain. Under natural smoothness conditions for the data and the location of the measurement points, the existence and uniqueness theorem local in time is demonstrated. The obtained solution to the problem is regular, i. e., all generalized derivatives included in the equation are summable to some power, and the equation holds almost everywhere. The method is constructive, and the approach allows to develop numerical methods for solving the problem. The proof is based on a priori estimates obtained and the fixed-point theorem.