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Abstract: This work investigates the inverse problem of reconstructing a spacewise dependent heat source in the parabolic heat equation using a final temperature measurement. Such problem has important application in a large field of applied science. On the basis of the optimal control framework, the existence and necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer are deduced from the necessary condition. The Landweber iteration algorithm is applied to the inverse problem and some numerical results are presented for various typical test examples. [Copyright &y& Elsevier]

Abstract: This paper studies an inverse problem of recovering the first-order coefficient in parabolic equation when the final observation is given. Such problem has important application in a large field of applied science. The original problem is transformed into an optimal control problem by the optimization theory. The existence, uniqueness and necessary condition of the minimum for the control functional are established. By an elliptic bilateral variational inequality which is deduced from the necessary condition, an algorithm and some numerical experiments are proposed in the paper. The numerical results show that the proposed method is an accurate and stable method to determine the coefficient of first-order in the inverse parabolic problems. [Copyright &y& Elsevier]