Mathematical model for optimal control in wastewater discharges: the global performance.

In this work we show how mathematical models and optimal control techniques can help us to solve some problems of environmental engineering, more precisely, water pollution problems arising from wastewater discharges into coastal areas or rivers. We deal with a complete two-dimensional mathematical model for the evolution of pollutant concentration in a shallow water domain. By integrating this model we obtain a zero-dimensional one and we use it to study the global performance of the system in a realistic situation. Finally, by using the two-dimensional model, we recall two optimal control problems related to the wastewater disposal problem.