Geodesic
A free boundary problem for a predator-prey model with nonlinear prey-taxis
Applications of Mathematics, Tome 63 (2018) no. 2, pp. 125-147.

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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.
DOI : 10.21136/AM.2018.0227-17
Classification : 35K51, 35K55, 35K57, 35K59, 35R35, 92B05, 92D25
Keywords: prey-predator model; prey-taxis; free boundary; classical solutions; global existence 
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Yousefnezhad, Mohsen; Mohammadi, Seyyed Abbas; Bozorgnia, Farid. A free boundary problem for a predator-prey model with nonlinear prey-taxis. Applications of Mathematics, Tome 63 (2018) no. 2, pp. 125-147. doi : 10.21136/AM.2018.0227-17. http://geodesic.mathdoc.fr/articles/10.21136/AM.2018.0227-17/

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