SOLVING A CROP PROBLEM BY AN OPTIMAL CONTROL METHOD

Maïtine Bergounioux (1) , Hem Raj Joshi (2) , Suzanne Sl Lenhart (3)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 Dept. of Mathematics and Computer Science
3 Department of Mathematics [Tennessee]

A system of ordinary differential equations coupled with a parabolic partial differential equation is studied in order to understand an interaction between two crops and a pathogen. Two different types of crops are planted in same field in some pattern so that the spread of pathogen can be controlled. The pathogen prefers to eat one crop. The other crop, which is not preferred by the pathogen, is introduced to control the spread of pathogen in the farming land. The “optimal” initial planting pattern is sought to maximize plant yields while minimizing the variation in the planting pattern. The optimal pattern is characterized by a variation inequality involving the solutions of the optimality system. Numerical examples are given to illustrate the results.

Mots clés: pathogen spread; Crop problem; optimal control; pathogen spread.

Domaines: Optimisation et contrôle [math.OC]

Maïtine Bergounioux, Hem Raj Joshi, Suzanne Sl Lenhart. SOLVING A CROP PROBLEM BY AN OPTIMAL CONTROL METHOD. Natural Resource Modeling, 2005, 18, number 3 pp 323-346. ⟨hal-00022001⟩