Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2014; 51(5): 1357-1368

Printed September 30, 2014

https://doi.org/10.4134/BKMS.2014.51.5.1357

Copyright © The Korean Mathematical Society.

Dynamical behavior of a harvest single species model on growing habitat

Zhi Ling and Lai Zhang

Yangzhou University, Ume{\aa} University

Abstract

This paper is concerned with a reaction-diffusion single speci\-es model with harvesting on $n$-dimensional isotropically growing domain. The model on growing domain is derived and the corresponding comparison principle is proved. The asymptotic behavior of the solution to the problem is obtained by using the method of upper and lower solutions. The results show that the growth of domain takes a positive effect on the asymptotic stability of positive steady state solution while it takes a negative effect on the asymptotic stability of the trivial solution, but the effect of the harvesting rate is opposite. The analytical findings are validated with the numerical simulations.

Keywords: growing domain, population model, asymptotic behavior

MSC numbers: 35K57, 92C15