A continuous‐time inverse operator for groundwater and contaminant transport modeling: Model identifiability

General identifiability conditions are derived for the model coefficients of the spatially discretized continuous‐time diffusion equation. These conditions in turn determine some sufficient and necessary conditions for the existence and uniqueness of the continuous‐time inverse operator described in a previous article. The identifiability conditions are in terms of the initial conditions and the flux vector containing boundary condition information and the eigenspace of the spatially discretized system. The derivation of these conditions gives some insight into the location of the solution of the inverse problem in terms of the direct operator under investigation in the space of the Laplace transform and limited insight into the stability of the solution near that location.