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Free Boundary Problems for a Lotka–Volterra Competition System

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Abstract

In this paper we investigate two free boundary problems for a Lotka–Volterra type competition model in one space dimension. The main objective is to understand the asymptotic behavior of the two competing species spreading via a free boundary. We prove a spreading-vanishing dichotomy, namely the two species either successfully spread to the right-half-space as time \(t\) goes to infinity and survive in the new environment, or they fail to establish and die out in the long run. The long time behavior of the solutions and criteria for spreading and vanishing are also obtained. This paper is an improvement and extension of Guo and Wu (J Dyn Differ Equ 24:873–895, 2012).

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Acknowledgments

Authors would like to thank the referee for helpful comments. This work was supported by NSFC Grants 11071049 and 11371113.

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Authors and Affiliations

  1. Natural Science Research Center, Harbin Institute of Technology, Harbin, 150080, People’s Republic of China

    Mingxin Wang & Jingfu Zhao

  2. School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong, 723000, People’s Republic of China

    Jingfu Zhao

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  1. Mingxin Wang
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  2. Jingfu Zhao
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Correspondence to Mingxin Wang.

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Wang, M., Zhao, J. Free Boundary Problems for a Lotka–Volterra Competition System. J Dyn Diff Equat 26, 655–672 (2014). https://doi.org/10.1007/s10884-014-9363-4

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  • DOI: https://doi.org/10.1007/s10884-014-9363-4

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