Abstract
We propose a simple model of landfill and study a minimal time control problem where the re-circulation leachate is the manipulated variable. We propose a scheme to construct the optimal strategy by dividing the state space into three subsets $\mathcal{E}_0$, $\mathcal{Z}_{1}$ and the complementary. On $\mathcal{E}_0$ and $\mathcal{Z}_{1}$, the optimal control is constant until reaching target, while it can exhibit a singular arc outside these two subsets. Moreover, the singular arc could have a {\em barrier}.In this case, we prove the existence of a switching curve that passes through a point of {\em prior saturation} under the assumption that the set $\mathcal{E}_0$ intersects the singular arc.Numerical computations allow then to determine the switching curve and depict the optimal synthesis.