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From the final and interior temperature measurements identifying the sourceterm with initial temperature simultaneously is an inverse heat conductionproblem which is a kind of ill-posed. The optimal control framework has beenfound to be effective in dealing with these problems. However, they require tofind the gradient information. This idea has been employed in this research. Wederive the gradient of Tikhonov functional and establish the stability of theminimizer from the necessary condition. The stability and effectiveness of theevolutionary algorithm are presented for various test examples.

An inverse problem in estimating the time dependent source term and  initial temperature simultaneously by the polynomial regression and conjugate  gradient method