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An Optimal Control Problem for a Predator-Prey Reaction-Diffusion System

Published online by Cambridge University Press:  13 September 2010

N. C. Apreutesei
N. C. Apreutesei*
Affiliation:
Department of Mathematics, Technical University "Gh. Asachi" Iasi, 11, Bd. Carol I 700506 Iasi, Romania
*
*Corresponding author: E-mail: napreut@gmail.com
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Abstract

An optimal control problem is studied for a predator-prey system of PDE, with a logistic growth rate of the prey and a general functional response of the predator. The control function has two components. The purpose is to maximize a mean density of the two species in their habitat. The existence of the optimal solution is analyzed and some necessary optimality conditions are established. The form of the optimal control is found in some particular cases.

Keywords

adjoint systemfunctional response of the predatorlogistic growth ratemaximum principleoptimality conditions
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 6: Ecology (Part 2) , 2010 , pp. 180 - 195
Copyright
© EDP Sciences, 2010

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