The Well-Posed Identification of the Interface Heat Transfer Coefficient Using an Inverse Heat Conduction Model

Abstract

In this study, the inverse problems of recovering the heat transfer coefficient at the interface of integral measurements are considered. The heat transfer coefficient occurs in the transmission conditions of an imperfect contact type. This is representable as a finite part of the Fourier series with time-dependent coefficients. The additional measurements are integrals of a solution multiplied by some weights. The existence and uniqueness of solutions in Sobolev classes are proven and the conditions on the data are sharp. These conditions include smoothness and consistency conditions on the data and additional conditions on the kernels of the integral operators used in the additional measurements. The proof relies on a priori bounds and the contraction mapping principle. The existence and uniqueness theorem is local in terms of time.