The constant growing of anthropogenic activities leads to a dete- rioration of water quality resources. In lakes, the accumulation of nutrients (as phosphorus) implies an algae development, including cyanobacteria, and thus a perturbation of the ecosystem : this is the eutrophication.
An optimal control problem for the lake eutrophication is considered. We model the dynamics of phosphorus stock and cyanobacteria concentration with coupled non- linear partial differential equations. Our control is only defined on the lake shore, thus leading to a Dirichlet boundary control problem. We discuss the originality of the model. We prove the well-posedness of the state problem and the existence of a global solution for the optimal control.
 C. Choquet and E. Comte, Optimal control of lake eutrophication. Journal of Mathematical Analysis and Applications, 528(2), 2023.
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