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Identification of injection and extraction wells from overspecified boundary data

In this paper, we focus on the identification of wells’ positions and fluxes/flows from the knowledge of overspecified data: hydraulic head and flux, on a part of the domain boundary. The used method is based on minimizing a constitutive law gap functional. We consider two inverse problems: in the first one overspecified conditions are available throughout the entire domain boundary; in the second inverse problem, in addition to the wells, boundary condition are also unknown on an inaccessible part of the domain boundary.