Minimax Optimization in Multidimensional Inverse Heat Conduction Problems

An approach to the solution of inverse problems of heat conduction in multidimensional spatial domain based on the theory of optimal control of objects with distributed parameters is proposed. Parametric optimization with minimax quality functional on given convergent compact sets is applied. On the basis of preliminary parametrization of desired characteristics using modal description of the process, the inverse problem is reduced to the problem of parametric optimization with respect to a finite-dimensional vector of parameters. The use of alternance properties of optimal states leads to a closed system of computational relations.This approach is applied to solve the inner inverse problem of finding the lumped function of power of heat sources and their spatially distributed pattern.