Analyse mathématique et contrôle optimal pour les équations d’advection-diffusion : Application au problème de transfert de nutriments pour les plantes en agroécologie

Abstract : Agriculture soils were highly contaminated for a long time by pesticides which were widely used by producers to fight against weevils. Soils where also contaminated by the use of fertilizers to increase the plant development. An ecological alternative using service plants is encouraged following recent research. The aim of this work is to give a mathematical and a modelling point of view as we study the mecha- nisms of nutrient transfer to plants using the mathematical analysis and optimal control theories. The two cases of polluted and non-polluted soils are considered. The nutrient transfer and uptake processes are modeled by an advection-diffusion system derived from the Nye-Tinker-Barber (NTB) model. The absorbed nutrient concentration represented by the Michaelis-Mention function at the root surface of the principal plant, depends on time and space. We study the existence of a solution for the linear and nonlinear NTB systems, then we characterize the opti- mal control which corresponds to the added nutrients from the service plant. For the pollution case, we use the concept of low-regret and no-regret control of J.-L. Lions.
Document type :
Theses
Complete list of metadatas

Cited literature [25 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-01405394
Contributor : Abes Star <>
Submitted on : Tuesday, November 29, 2016 - 7:26:06 PM
Last modification on : Friday, May 17, 2019 - 1:19:54 AM
Long-term archiving on : Monday, March 27, 2017 - 7:17:15 AM

File

LOUISON_Loic.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-01405394, version 1

Citation

Loïc Louison. Analyse mathématique et contrôle optimal pour les équations d’advection-diffusion : Application au problème de transfert de nutriments pour les plantes en agroécologie. Mathématiques générales [math.GM]. Université de Guyane, 2015. Français. ⟨NNT : 2015YANE0001⟩. ⟨tel-01405394⟩

Share

Metrics

Record views

453

Files downloads

287