A Free Boundary Problem for a Predator-Prey Model with Nonlinear Prey-Taxis

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 sy...

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Veröffentlicht in:	Applications of Mathematics 2018-04, Vol.63 (2), p.125-147
Hauptverfasser:	Yousefnezhad, Mohsen, Mohammadi, Seyyed Abbas, Bozorgnia, Farid
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Applications of Mathematics Classical and Continuum Physics Computer simulation Free boundaries Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical models Mathematics Mathematics and Statistics Numerical analysis Optimization Predator-prey simulation System theory Theoretical
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Beschreibung
Zusammenfassung:	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.
ISSN:	0862-7940 1572-9109
DOI:	10.21136/AM.2018.0227-17