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

Mohsen Yousefnezhad; Seyyed Abbas Mohammadi; Farid Bozorgnia

Applications of Mathematics (2018)

  • Volume: 63, Issue: 2, page 125-147
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Yousefnezhad, Mohsen, Mohammadi, Seyyed Abbas, and Bozorgnia, Farid. "A free boundary problem for a predator-prey model with nonlinear prey-taxis." Applications of Mathematics 63.2 (2018): 125-147. <http://eudml.org/doc/294582>.

@article{Yousefnezhad2018,
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.},
author = {Yousefnezhad, Mohsen, Mohammadi, Seyyed Abbas, Bozorgnia, Farid},
journal = {Applications of Mathematics},
keywords = {prey-predator model; prey-taxis; free boundary; classical solutions; global existence},
language = {eng},
number = {2},
pages = {125-147},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A free boundary problem for a predator-prey model with nonlinear prey-taxis},
url = {http://eudml.org/doc/294582},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Yousefnezhad, Mohsen
AU - Mohammadi, Seyyed Abbas
AU - Bozorgnia, Farid
TI - A free boundary problem for a predator-prey model with nonlinear prey-taxis
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 2
SP - 125
EP - 147
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.
LA - eng
KW - prey-predator model; prey-taxis; free boundary; classical solutions; global existence
UR - http://eudml.org/doc/294582
ER -

References

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