An optimal control problem for a pest, predator, and plant system

The paper is devoted to an optimal control problem for a system of three nonlinear parabolic equations from population dynamics. The equations model a trophic chain consisting of a predator, a pest and a plant species. The existence and uniqueness of the positive solution for the system are proved....

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2012-06, Vol.13 (3), p.1391-1400
Main Author: Apreutesei, N.C.
Format: Article
Language:English
Subjects:
Density
Dual system
Dynamical systems
First order optimality conditions
Mathematical analysis
Mathematical models
Nonlinear dynamics
Optimization
Pests
Predators
Reaction–diffusion equations
Second order optimality conditions
Trophic chain
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Summary:The paper is devoted to an optimal control problem for a system of three nonlinear parabolic equations from population dynamics. The equations model a trophic chain consisting of a predator, a pest and a plant species. The existence and uniqueness of the positive solution for the system are proved. The control variable is connected with the action of a pesticide. Our goal is to minimize the density of the pest and to maximize the plant density. The existence of the optimal solution is proved. The first and second order optimality conditions are established.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2011.11.004