A free boundary problem for a prey-predator model with degenerate diffusion and predator-stage structure

Siyu Liu; Haomin Huang; Mingxin Wang

doi:10.3934/dcdsb.2019245

Article Contents

2020, Volume 25, Issue 5: 1649-1670. Doi: 10.3934/dcdsb.2019245

This issue Previous Article Stability and bifurcation analysis of Filippov food chain system with food chain control strategy Next Article A nonlinear Stefan problem with variable exponent and different moving parameters

A free boundary problem for a prey-predator model with degenerate diffusion and predator-stage structure

1.
School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2.
Department of Mathematics, Southern University of Science and Technology, Shenzhen 518000, China
3.
School of Mathematics and Statistics, Wuhan University, Wuhan 430000, China

^* Corresponding author: Mingxin Wang (mxwang@hit.edu.cn)
^* Corresponding author: Mingxin Wang (mxwang@hit.edu.cn)

Received: February 28, 2019

Revised: May 31, 2019

Early access: November 2019

Published: May 2020

This work is supported by NSFC Grants 11771110, 11971128

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Abstract

In this paper we consider a free boundary problem for a prey-predator model with degenerate diffusion and predator-stage structure. In our model, the individuals of a new or invasive predatory species are classified as belonging to either the immature or mature case. Firstly, the global existence, uniqueness, regularity of the solution are derived. And then when vanishing happens, we get uniform estimates and the long time behavior of the solution. At last, a sharp criterion governing spreading and vanishing for the free boundary problem is studied by the upper and lower solution method.

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Mathematics Subject Classification: Primary: 35A01, 35K65, 35R35, 35B40, 92D25.

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