Determination of the reaction coefficient in a time dependent nonlocal diffusion process. (14th January 2021) - Ding, Ming-Hui; Zheng, Guang-Hui
Abstract: This paper investigates the inverse reaction coefficient problem for a time dependent nonlocal diffusion equation by utilizing the nonlocal flux measurement from an accessible part of region, which is a continuation and an extension of our recent work (Zheng and Ding 2020 Inverse Problems 36 035006). The uniqueness of inverse reaction coefficient problem is proved. The variational regularization method is proposed to overcome the ill-posedness of inverse problem, and an alternating iteration method is adopted to automatically select regularization parameters. Furthermore, we use Laplace approximation method to capture the statistics information of the solution. In particular, we prove the lower bound of confidence width is rigorously estimated to characterize the reliability of the method. Finally, numerical results indicate that the proposed method could yield an accurate estimate and efficient uncertainty quantification of the solution.