Reconstruction of the Stefan–Boltzmann coefficients in a heat-transfer process

In this paper, we investigate an inverse problem of determining the coefficients within the framework of Stefan–Boltzmann radiation boundary conditions for the heat-transfer process in a material. A mathematical formulation for the forward and inverse problems is introduced and the uniqueness of the inverse problem is proved. The finite-difference method is utilized for the discretization of the forward problem. Based on our analysis, we propose a fast-reconstruction method for solving the inverse problem, which can be easily realized in practice. Some regularization techniques are implemented to overcome the ill-posedness of the problem. Numerical simulation shows that our reconstruction method is stable and effective.