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This paper deals with an inverse problem of identifying the source coefficient in degenerate parabolic equations. On the basis of extremum principle, the uniqueness of the proposed problem is obtained. The difference scheme for the direct problem is got by using the finite volume method and the corresponding stability is also proved. An iteration scheme of the Landweber type is applied to handle the numerical solution. In the end, several numerical experiments are performed to test the validity of the scheme. The numerical results show that the method is stable and the unknown function is recovered very well when iterative parameter α and iterative times are matching appropriately. [ABSTRACT FROM AUTHOR]

The aim of this work is to reconstruct a spacewise dependent heat source in a degenerate heat equation using the final measurement temperature. Based on the optimal control framework, the inverse problem is transformed into an optimization problem. The existence and necessary condition of the minimizer for the cost functional are established, and the global uniqueness and stability of the minimizer are also obtained from the necessary condition. Finally, a numerical algorithm on the basis of the conjugate gradient method is designed to treat the inverse problem and some numerical experiments are also performed. The numerical results show that the algorithm designed in the paper is quite efficient and stable, and the unknown heat source is recovered very well. [ABSTRACT FROM AUTHOR]