An inverse problem for a quasi-static approximate model of radiative heat transfer

We consider an inverse problem for a system of equations modeling quasi-static conductive and radiative heat transfer. The problem consists in finding the right-hand side of the heat transfer equation, which is a linear combination of given functionals. The prescribed data are the values of these functionals evaluated on the solution. The solvability of the problem is proven without any smallness assumptions on the model parameters. In the class of bounded temperature fields, the uniqueness of the solution of the inverse problem is shown. Further, we study the Tikhonov regularization in the framework of a PDE constrained optimization problem and show that the approximating sequence contains a convergent subsequence. The analytical results depend crucially on new and refined a priori estimates for the solutions. (C) 2018 Elsevier Inc. All rights reserved.