Analysis of a toy model for optimal crop protection

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  • 9 May 2025
    • preprint
    • Published by HAL in HAL
Abstract
In this paper we investigate an optimal control problem involving a toy model for the protection on a crop eld. Precisely, we consider a protection on a crop eld and we want to place intervention zones represented by a control, in order to maximise the protection on the eld during a given period. Using a relaxation method, we prove that there exists a control which maximises the protection and, moreover, it must be a bang-bang control. Furthermore, with additional assumptions on the crop eld geometry, some results on the shape of the optimal intervention are proved using comparison results for elliptic equations via Schwarz and Steiner symmetrizations. Finally, some numerical simulations are performed in order to illustrate those results.

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