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

TY - JOUR

T1 - A Free Boundary Problem for a Predator-Prey Model with Nonlinear Prey-Taxis

AU - Yousefnezhad, Mohsen

AU - Mohammadi, Seyyed Abbas

AU - Bozorgnia, Farid

PY - 2018/3/28

Y1 - 2018/3/28

N2 - 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.

AB - 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.

KW - pre-predator model

KW - prey-taxis

KW - Free boundary

KW - classic solutions

KW - global existence

UR - https://www.scopus.com/pages/publications/85046253522

U2 - 10.21136/AM.2018.0227-17

DO - 10.21136/AM.2018.0227-17

M3 - Article

SN - 0862-7940

VL - 63

SP - 125

EP - 147

JO - Applications of Mathematics

JF - Applications of Mathematics

IS - 2

ER -