Identification of the heat transfer coefficient from boundary integral data

We consider a second order parabolic equation and the well-posedness of inverse problems of recovering the heat transfer coefficients in Sobolev spaces with the use of a collection of integrals of a solution over the boundary of a domain. Under certain conditions on the data, we demonstrate that the existence of a unique local-in-time solution that depends continuously on the data. The method is constructive and allows us to provide some numerical methods of solution. The proof employs a priori estimates and the fixed point theorem.