  We study minimal time strategies for the treatment of pollution of large
volumes, such as lakes or natural reservoirs, with the help of an autonomous
bioreactor. The control consists in feeding the bioreactor from the resource,
the clean output returning to the resource with the same flow rate. We first
characterize 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. With the help of the Maximum Principle, we show that the
optimal control law is non-monotonic and terminates with a constant phase,
contrary to the homogeneous case for which the optimal flow rate is decreasing
with time. This study allows the decision makers to identify situations for
which the benefit of using non-constant flow rates is significant.
