Optimal control of harvesting coupled with boundary control in a predator-prey system. (English) Zbl 1014.92040
Summary: We consider boundary control and control via harvesting in a parabolic predator-prey system for a bounded region. The boundary control depicts the relationship between the boundary environment and the possibly harmful species. In addition, a proportion of the predator is harvested for profit. We choose to maximize the objective functional which incorporates the amount of the prey and the revenue of harvesting of the predator and less the economic cost of sustaining a satisfactory boundary habitat and the cost due to the harvesting component. Moreover, we characterize the unique optimal control in terms of the solution to the optimality system, which is the state system coupled with the adjoint system.
MSC:
| 92D40 | Ecology |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 49N90 | Applications of optimal control and differential games |
| 92D25 | Population dynamics (general) |
Keywords:
parabolic predator-prey systemReferences:
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