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Coexistence and optimal control problems for a degenerate predator-prey model. (English) Zbl 1210.49042

Summary: We present a predator-prey mathematical model for two biological populations which dislike crowding. The model consists of a system of two degenerate parabolic equations with nonlocal terms and drifts. We provide conditions on the system ensuring the periodic coexistence, namely the existence of two non-trivial non-negative periodic solutions representing the densities of the two populations. We assume that the predator species is harvested if its density exceeds a given threshold. A minimization problem for a cost functional associated with this process and with some other significant parameters of the model is also considered.

MSC:

49N75 Pursuit and evasion games
91A24 Positional games (pursuit and evasion, etc.)
35K65 Degenerate parabolic equations
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