Determination of the characteristics of concentrated heat sources in a half-space under prescribed conditions for the heat exchange and temperature distribution on its surface

A method is given for solving the inverse problem for determining the intensity and location of concentrated heat sources in a half-space under prescribed conditions on the heat exchange with the external medium and a distribution of surface temperature with error. Using methods of the variational calculus, we obtain a system of nonlinear equations for the characteristics of subsurface heat sources, leading to a temperature function on the surface which is closest to the given distribution. Several individual examples are solved.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 29, pp. 46–51, 1989.