| Issue |
Math. Model. Nat. Phenom.
Volume 5, Number 6, 2010
Ecology (Part 2)
|
|
|---|---|---|
| Page(s) | 180 - 195 | |
| DOI | https://doi.org/10.1051/mmnp/20105609 | |
| Published online | 13 September 2010 | |
An Optimal Control Problem for a Predator-Prey Reaction-Diffusion System
Department of Mathematics, Technical University "Gh. Asachi"
Iasi, 11, Bd. Carol
I
700506
Iasi, Romania
* Corresponding author: E-mail:
napreut@gmail.com
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.
Mathematics Subject Classification: 9K20 / 92D25 / 93C10 / 93C15 / 35K50 / 35K55
Key words: adjoint system / functional response of the predator / logistic growth rate / maximum principle / optimality conditions
© EDP Sciences, 2010
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