Applications of Mathematics, Vol. 63, No. 2, pp. 125-147, 2018


A free boundary problem for a predator-prey model with nonlinear prey-taxis

Mohsen Yousefnezhad, Seyyed Abbas Mohammadi, Farid Bozorgnia

Received August 19, 2017.   First published March 28, 2018.

Abstract:  This paper deals with a reaction-diffusion system modeling a free boundary problem of the predator-prey type with prey-taxis over a one-dimensional habitat. The free boundary represents the spreading front of the predator species. The global existence and uniqueness of classical solutions to this system are established by the contraction mapping principle. With an eye on the biological interpretations, numerical simulations are provided which give a real insight into the behavior of the free boundary and the stability of the solutions.
Keywords:  prey-predator model; prey-taxis; free boundary; classical solutions; global existence
Classification MSC:  35K57, 35K55, 35R35, 92B05
DOI:  10.21136/AM.2018.0227-17


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Affiliations:   Mohsen Yousefnezhad (corresponding author), School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran, e-mail: yousefnezhad@ipm.ir; Seyyed Abbas Mohammadi, Department of Mathematics, College of Sciences, Yasouj University, Yasouj, 75918-74934, Iran, e-mail: mohammadi@yu.ac.ir; Farid Bozorgnia, Department of Mathematics, School of Science and Technology, Örebro University, Örebro, SE-701 82, Sweden, e-mail: farid.bozorgnia@oru.se

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