Résumé
In this paper, we study the optimization problem of maximizing biogas production at the steady state in a two-stage anaerobic digestion model, which was initially proposed in [4]. Nominal operating points, consisting in steady states where the involved microorganisms coexist, are usually referred to as desired operational conditions, in particular for maximizing biogas production. Nevertheless, we prove that under some conditions related to input substrate concentrations and microorganism growth functions, the optimal steady state can be the extinction of one of the two species. We provide some numerical examples of this situation.