A free boundary problem for some modified predator-prey model in a higher dimensional environment

Hongmei Cheng; Qinhe Fang; Yang Xia

Applications of Mathematics (2022)

  • Volume: 67, Issue: 5, page 615-632
  • ISSN: 0862-7940

Abstract

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We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated by the prey. This free boundary problem is used to describe the spreading of a new introduced predator. We first establish that a spreading-vanishing dichotomy holds for this model. Namely, the predator either successfully spreads to the entire space as t goes to infinity and survives in the new environment, or it fails to establish and dies out in the long term. The longterm behavior of the solution and the criteria for spreading and vanishing are also obtained. Moreover, when spreading of the predator happens, we provide some rough estimates of the spreading speed.

How to cite

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Cheng, Hongmei, Fang, Qinhe, and Xia, Yang. "A free boundary problem for some modified predator-prey model in a higher dimensional environment." Applications of Mathematics 67.5 (2022): 615-632. <http://eudml.org/doc/298473>.

@article{Cheng2022,
abstract = {We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated by the prey. This free boundary problem is used to describe the spreading of a new introduced predator. We first establish that a spreading-vanishing dichotomy holds for this model. Namely, the predator either successfully spreads to the entire space as $t$ goes to infinity and survives in the new environment, or it fails to establish and dies out in the long term. The longterm behavior of the solution and the criteria for spreading and vanishing are also obtained. Moreover, when spreading of the predator happens, we provide some rough estimates of the spreading speed.},
author = {Cheng, Hongmei, Fang, Qinhe, Xia, Yang},
journal = {Applications of Mathematics},
keywords = {free boundary; predator-prey model; spreading-vanishing dichotomy; spreading speed},
language = {eng},
number = {5},
pages = {615-632},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A free boundary problem for some modified predator-prey model in a higher dimensional environment},
url = {http://eudml.org/doc/298473},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Cheng, Hongmei
AU - Fang, Qinhe
AU - Xia, Yang
TI - A free boundary problem for some modified predator-prey model in a higher dimensional environment
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 5
SP - 615
EP - 632
AB - We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated by the prey. This free boundary problem is used to describe the spreading of a new introduced predator. We first establish that a spreading-vanishing dichotomy holds for this model. Namely, the predator either successfully spreads to the entire space as $t$ goes to infinity and survives in the new environment, or it fails to establish and dies out in the long term. The longterm behavior of the solution and the criteria for spreading and vanishing are also obtained. Moreover, when spreading of the predator happens, we provide some rough estimates of the spreading speed.
LA - eng
KW - free boundary; predator-prey model; spreading-vanishing dichotomy; spreading speed
UR - http://eudml.org/doc/298473
ER -

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