Identification of the source function for a seawater intrusion problem in unconfined aquifer

In this work, we study the inverse source problem of a seawater intrusion problem in an unconfined aquifer with sharp-diffuse interfaces. The model associated with the direct problem is nonlinear. We aim to reconstruct the source term following the technique used in [10]. As this technique is based on variable separation, a fixed-point strategy is adopted to linearize the problem. Numerical convergence is proven using some examples.