The backward problem of anomalous subdiffusion for gas transport in porous coal matrix

Abstract In this paper we study the backward problem for multi-term time-fractional diffusion equation with Robin boundary. First, we prove the regularity of the solution for the direct problem and analyse the ill-posedness of the backward problem. Furthermore, we prove the continuity of the forward mapping with respect to the initial value. Then, the iterative regularizing ensemble Kalman method is applied to determine the unknown parameters. Finally, the effectiveness and robustness of IREKM in dealing with noisy data are verified by means of three numerical examples.