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A Free Boundary Problem for a Leslie-Gower Predator-Prey Model in Higher Dimensions and Heterogeneous Environment
American Journal of Applied Mathematics
Volume 8, Issue 5, October 2020, Pages: 284-292
Received: Sep. 14, 2020; Accepted: Oct. 12, 2020; Published: Oct. 26, 2020
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Authors
Shiwen Niu, School of Mathematics and Statistics, Shandong Normal University, Jinan, P. R. China
Hongmei Cheng, School of Mathematics and Statistics, Shandong Normal University, Jinan, P. R. China
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Abstract
This paper is mainly concerned with some free boundary problems for a modified Leslie-Gower predator-prey model in higher dimensional and heterogeneous environment. To keep it simple in this article, we assume that the environment and solutions are all radially symmetric. We consider the problem which be used to describe the spreading of an introduced predator species in higher dimensional and heterogeneous environment. We will assume that the prey is initially uniformly well disturbed. The prey undergoes the diffusion and growth in the entire space R^n. The predator is initially introduced in some localized location. We establish that a spreading-vanishing dichotomy is held for this model. We use the comparison principle. we will give the existence, uniqueness and some estimates of the solution to the problem. We study the asymptotic behavior of two species evolving. The free boundary represents the spreading front of the predator species. The boundary condition is described by classic Stefan-like condition. It is proved that the problem addressed is well posed, and that the predator species disperses to all domains in finite time. The long time behaviors of solution and criteria for spreading and vanishing of predator species are also provided. Furthermore, in the case that spreading of predator species happens, we deduce some rough estimates of the spreading speed.
Keywords
Free Boundary, Predator-Prey Model, Spreading-Vanishing Dichotomy, Spreading Speed, Heterogeneous Environment
To cite this article
Shiwen Niu, Hongmei Cheng, A Free Boundary Problem for a Leslie-Gower Predator-Prey Model in Higher Dimensions and Heterogeneous Environment, American Journal of Applied Mathematics. Vol. 8, No. 5, 2020, pp. 284-292. doi: 10.11648/j.ajam.20200805.17
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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