Abstract
The aim of this chapter is to present an extension of the inverse problem methods to non-traditional heat transfer. It discusses the mathematical aspects of an identification problem for determining the nonlinear boundary condition in the heat transfer described by parabolic hemivariational inequalities (HVIs). Further, an identification problem for determining the nonlinear boundary condition in the nonstationary heat equation from the measurements, which are available in the interior or at the surface of a body, is considered. The existence and uniqueness of a solution to the direct problem, which is modeled by a parabolic HVI, is proved and its discretization is presented. Next, the approximation of the identification problem is analyzed, and the relationships between the approximate and the initial identification problems are established.
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