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

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 5, Issue: 6, page 180-195
- ISSN: 0973-5348

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topApreutesei, N. C.. "An Optimal Control Problem for a Predator-Prey Reaction-Diffusion System." Mathematical Modelling of Natural Phenomena 5.6 (2010): 180-195. <http://eudml.org/doc/197665>.

@article{Apreutesei2010,

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.},

author = {Apreutesei, N. C.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {adjoint system; functional response of the predator; logistic growth rate; maximum principle; optimality conditions; functional response of predators},

language = {eng},

month = {9},

number = {6},

pages = {180-195},

publisher = {EDP Sciences},

title = {An Optimal Control Problem for a Predator-Prey Reaction-Diffusion System},

url = {http://eudml.org/doc/197665},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Apreutesei, N. C.

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

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/9//

PB - EDP Sciences

VL - 5

IS - 6

SP - 180

EP - 195

AB - 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.

LA - eng

KW - adjoint system; functional response of the predator; logistic growth rate; maximum principle; optimality conditions; functional response of predators

UR - http://eudml.org/doc/197665

ER -

## References

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- A. Pazy. Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, 44. New York etc., Springer- Verlag, 1983. Zbl0516.47023
- S. Xu. Existence of global solutions for a predator-prey model with cross-diffusion. Electron. J. Diff. Eqns., (2008), 1-14. Zbl1138.35349
- S. Yosida. Optimal control of prey-predator systems with Lagrange type and Bolza type cost functionals. Proc. Faculty Science Tokai Univ., 18 (1983), 103-118. Zbl0541.49003

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