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Reconstruction of the Stefan-Boltzmann coefficients in a heat-transfer process. (English) Zbl 1236.35202

Summary: 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 simulations show that our reconstruction method is stable and effective.

MSC:

35R30 Inverse problems for PDEs
35Q79 PDEs in connection with classical thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)
80A23 Inverse problems in thermodynamics and heat transfer
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