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Zbl 1210.49042
Allegretto, W.; Fragnelli, G.; Nistri, P.; Papini, D.
Coexistence and optimal control problems for a degenerate predator-prey model. (English)
[J] J. Math. Anal. Appl. 378, No. 2, 528-540 (2011). ISSN 0022-247X

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 2000:: *49N75 Pursuit and evasion games
91A24 Positional games
35K65 Parabolic equations of degenerate type

Keywords: degenerate parabolic equations; positive periodic solutions; optimal control problems

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