Reconstruction of the heat transfer coefficient from boundary measurements

Abstract Well-posedness questions of reconstruction of the heat transfer coefficients from boundary measurements are considered. The additional measurements are the integrals of a solution with weights over the boundary of a domain. The inverse problem theory is involved. The heat transfer coefficient is sought in the form of a finite segment of the series with unknown Fourier coefficients depending on time. They satisfy a system of integral equations of Volterra type. It is demonstrated that, under certain conditions, a solution to the problem is uniquely determined locally in time and depends continuously on the data of the problem. These conditions include smoothness and compatibility conditions on the data and additional conditions on the kernels of the integral operators used in the additional measurements. The method is constructive and allows to provide a numerical algorithm for solving the problem. The proof rely on a priori estimates and the contraction mapping principle.