About optimal control problems for the bioremediation of natural water resources
Résumé
Several simple models that couple a waster-water treatment in a bioreactor with the dynamics of natural water resources (such as lakes, ground tables...) will be considered, depending on the number and locations of the pumps, and inhomogeneity assumptions. The optimal control problems consist in piloting the pumps for reaching a low pollution threshold in the water resource in minimal time. These problems present some technicalities such as a lack of convexity, and exhibit some non-intuitive features such as a non-monotonic dependency of the value function with respect to the diffusion parameter.