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Journal Articles SIAM Journal on Control and Optimization Year : 2022

A Game Theory Approach for the Groundwater Pollution Control

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Abstract

A differential game modeling the noncooperative outcome of pollution in groundwater is studied. Spatio-temp oral objectives are constrained by a convection-diffusion-reaction equation ruling the spread of the pollution in the aquifer, and the velocity of the flow solves an elliptic partial differential equation. The existence of a Nash equilibrium is proved using a fixed point strategy. A uniqueness result for the Nash equilibrium is also proved under some additional assumptions. Some numerical illustrations are provided.

Dates and versions

hal-03739654 , version 1 (28-07-2022)

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Emmanuelle Augeraud-Véron, Catherine Choquet, Éloïse Comte, Moussa Diédhiou. A Game Theory Approach for the Groundwater Pollution Control. SIAM Journal on Control and Optimization, 2022, 60 (3), pp.1667-1689. ⟨10.1137/19M1278223⟩. ⟨hal-03739654⟩
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