Periodic optimal control for parabolic Volterra-Lotka type equations. (English) Zbl 0818.49002
Summary: This paper considers the optimal harvesting control of a biological species whose growth is governed by the parabolic diffusive Volterra- Lotka equation. We prove that such equation with \(L^ \infty\) periodic coefficients has a unique positive periodic solution. We show the existence and uniqueness of an optimal control, and under certain conditions we characterize the optimal control in terms of a parabolic optimality system. A monotone sequence which converges to the optimal control is constructed.
MSC:
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 35K55 | Nonlinear parabolic equations |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 92D40 | Ecology |
| 35Q80 | Applications of PDE in areas other than physics (MSC2000) |
Keywords:
optimal harvesting control; parabolic diffusive Volterra-Lotka equation; existence; uniqueness; parabolic optimality systemReferences:
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