We study a mathematical model of anaerobic digestion with biomass recirculation, dedicated to landfill problems, and analyze its asymptotic behavior. We show that the global attractor is composed of an infinity of non-hyperbolic equilibria. For non-monotonic growth functions, this set is non connected, which impacts the performances of the bioprocess.

In a previous study, the two nitrifying functions (ammonia oxidizing bacteria (AOB) or nitrite-oxidizing bacteria (NOB)) of a nitrification reactor—operated continuously over 525 days with varying inputs—were assigned using a mathematical modeling approach together with the monitoring of bacterial phylotypes. Based on these theoretical identifications, we develop here a chemostat model that does not explicitly include only the resources’ dynamics (different forms of soluble nitrogen) but also explicitly takes into account microbial inter- and intra-species interactions for the four dominant phylotypes detected in the chemostat. A comparison of the models obtained with and without interactions has shown that such interactions permit the coexistence of two competing ammonium-oxidizing bacteria and two competing nitrite-oxidizing bacteria in competition for ammonium and nitrite, respectively. These interactions are analyzed and discussed.

We address the problem of the optimal control of in situ decontamination of water resources. We review several modeling, simulation and optimization techniques for this problem and their results. We show the benefit of combining tools from finite dimensional optimal control theory and numerical simulations of hydrodynamics equations, for providing simple and efficient feedback strategies. RésuméNous considérons le problème de commande optimale d’une décontamination in situ de ressources hydriques. Nous passons en revue différentes techniques de modélisation, simulation et optimisation pour ce problème, ainsi que leurs résultats. Nous montrons le bénéfice à combiner les outils de la théorie de la commande optimale en dimension finie avec la simulation numérique des équations de l’hydrodynamique, afin de fournir des stratégies par retour d’état à la fois simples et efficaces.

We study a mathematical model of anaerobic digestion with biomass recirculation, dedicated to landfill problems, and analyze its asymptotic behavior. We show that the global attractor is composed of an infinity of non-hyperbolic equilibria. For non-monotonic growth function, this feature has impacts on the performances of the bioprocess.