Optimization method for the inverse problem of reconstructing the source term in a parabolic equation
The authors consider an inverse problem of reconstructing in the parabolic heat equation a heat source term which depends on the spatial variable using a final temperature measurement. The authors use an optimal control framework to discuss this problem. The existence and a necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer for the cost functional are proved. The Landweber iteration algorithm is applied to the inverse problem and some numerical results are also presented.
scientific article; zbMATH DE number 5633807
scientific article