Accounting for spatial inhomogeneity in the minimal-time bioremediation of natural water resources
Résumé
We first present the results of a former paper that characterizes the optimal policies among constant and feedback controls, under the assumption of a uniform concentration in the resource. In a second part, we study the influence of an inhomogeneity in the resource, considering two measurements points.
We end with a presentation of numerical results in which the spatial inhomogeneity is simulated thanks to the Navier-Stokes equations for incompressible fluids. In this case the optimal strategy seems much more difficult to obtain. However, the numerical simulations provide an interesting tool to choose one suboptimal strategy or another.