Analysis of a toy model for optimal crop protection
Abstract
In this paper we investigate an optimal control problem involving a toy model for the protection on a crop field. Precisely, we consider a protection on a crop field and we want to place intervention zones represented by a control, in order to maximise the protection on the field 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 field 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.
Keywords
Cite
@article{arxiv.2410.11733,
title = {Analysis of a toy model for optimal crop protection},
author = {Luis Almeida and Aymeric Jacob de Cordemoy and Ayman Moussa and Nicolas Vauchelet},
journal= {arXiv preprint arXiv:2410.11733},
year = {2025}
}
Comments
21 pages