# An optimization problem related to water artificial recirculation for controlling eutrophication

## TL;DR

This paper introduces an optimal control framework for water recirculation aimed at preventing eutrophication in large waterbodies, combining nonlinear hydrodynamics and ecological models with numerical solutions.

## Contribution

It presents a novel coupled PDE model for water recirculation and eutrophication control, along with existence analysis and an efficient numerical algorithm.

## Key findings

- Numerical results demonstrate the effectiveness of the proposed control strategy.
- The model successfully captures complex interactions in water quality dynamics.
- The approach provides a practical tool for environmental management.

## Abstract

In this work, the artificial recirculation of water is presented and analyzed, from the perspective of the optimal control of partial differential equations, as a tool to prevent eutrophication effects in large waterbodies. A novel formulation of the environmental problem, based on the coupling of nonlinear models for hydrodynamics, water temperature and concentrations of the different species involved in the eutrophication processes, is introduced. After a complete and rigorous analysis of the existence of optimal solutions, a full numerical algorithm for their computation is proposed. Finally, some numerical results for a realistic scenario are shown, in order to prove the efficiency of our approach.