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Optimal harvesting-coefficient control of steady-state prey-predator diffusive Volterra-Lotka systems. (English) Zbl 0820.49011
The paper examines optimal harvesting of two interacting, via Volterra- Lotka equations, populations with diffusion. The optimality criterion is the maximal sustainable yield. Existence and uniqueness of solutions of the original controlled systems are verified under natural conditions. Optimality equations are displayed and analyzed. A monotone solution scheme is set along with approximation estimates.

MSC:
49K20 Optimality conditions for problems involving partial differential equations
92D40 Ecology
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
35J35 Variational methods for higher-order elliptic equations
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