Asymptotical methods for optimal control problems. Examples for the groundwater management

30 Aug 2018, 16:10
45m
LILLIAD Learning Center

LILLIAD Learning Center

Cité Scientifique, Villeneuve d'Ascq

Speaker

Prof. Catherine Choquet (Université de La Rochelle)

Description

This talk aims at illustrating some methods for the asymptotical analysis of optimal contribution-ol problems. We use examples in the context of groundwater pollution. The spatio-temporal objective takes into account the economic trade off between the pollutant use –for instance fertilizer– and the cleaning costs. It is constrained by a hydrogeological PDEs model for the spread of the pollution in the aquifer. We rigorously derive, by asymptotic analysis, the effective optimal control problem for contaminant species that are slightly concentrated in the aquifer. On the other hand, the mathematical analysis of the optimal control problems is performed and we prove in particular that the latter effective problem is well-posed. Furthermore, a stability property of the optimal control process is provided: any optimal solution of the properly scaled problem tends to the optimal solution of the effective problem as the characteristic pollutant concentration decreases. Finally we give some results in game theory.

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