# American Institute of Mathematical Sciences

June  2015, 4(2): 193-203. doi: 10.3934/eect.2015.4.193

## Modeling plant nutrient uptake: Mathematical analysis and optimal control

 1 UMR Espace-Dev, Université de la Guyane, UR, UM2, IRD, 2091 Route de Baduel, 97306 Cayenne (Guyane), France 2 UMR Espace-Dev, Université de la Guyane, UR, UM2, IRD, Campus de TrouBiran, Route de Baduel, 97337 Cayenne (Guyane), France 3 INRA, UR1321, ASTRO AgroSystèmes TROpicaux, 97170 Petit-Bourg (Guadeloupe), France 4 INRA, UMR 1391 ISPA, F-33140 Villenave d’Ornon, France

Received  April 2014 Revised  September 2014 Published  May 2015

The article studies the nutrient transfer mechanism and its control for mixed cropping systems. It presents a mathematical analysis and optimal control of the absorbed nutrient concentration, governed by a transport-diffusion equation in a bounded domain near the root system, satisfying to the Michaelis-Menten uptake law.
The existence, uniqueness and positivity of a solution (the absorbed concentration) is proved. We also show that for a given plant we can determine the optimal amount of required nutrients for its growth. The characterization of the optimal control leading to the desired concentration at the root surface is obtained. Finally, some numerical simulations to evaluate the theoretical results are proposed.
Citation: Loïc Louison, Abdennebi Omrane, Harry Ozier-Lafontaine, Delphine Picart. Modeling plant nutrient uptake: Mathematical analysis and optimal control. Evolution Equations & Control Theory, 2015, 4 (2) : 193-203. doi: 10.3934/eect.2015.4.193
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