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

Applications of mathematics

Seyyed Abbas Mohammadi^2¹  Farid Bozorgnia^3²  Mohsen Yousefnezhad^1³ 

[1]Department of Mathematics, College of Sciences, Yasouj University, Yasouj, 75918-74934, Iran^2

[2]Department of Mathematics, School of Science and Technology, Örebro University, Örebro, SE-701 82, Sweden^3

[3]School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran^1

关键词: prey-predator model;    prey-taxis;    free boundary;    classical solutions;    global existence;   

DOI  :  10.21136/AM.2018.0227-17

学科分类：应用数学

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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.

【 授权许可】

Unknown