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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.
49N75Pursuit and evasion games in calculus of variations
91A24Positional games
35K65Parabolic equations of degenerate type
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