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Spreading with two speeds and mass segregation in a diffusive competition system with free boundaries

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Abstract

We investigate the spreading behavior of two invasive species modeled by a Lotka–Volterra diffusive competition system with two free boundaries in a spherically symmetric setting. We show that, for the weak–strong competition case, under suitable assumptions, both species in the system can successfully spread into the available environment, but their spreading speeds are different, and their population masses tend to segregate, with the slower spreading competitor having its population concentrating on an expanding ball, say \(B_t\), and the faster spreading competitor concentrating on a spherical shell outside \(B_t\) that disappears to infinity as time goes to infinity.

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Acknowledgements

The authors are grateful to the referee for valuable suggestions on improving the presentation of the paper. YD was supported by the Australian Research Council and CHW was partially supported by the Ministry of Science and Technology of Taiwan under the grant MOST 105-2628-M-024-001-MY2 and National Center for Theoretical Science (NCTS). This research was initiated during the visit of CHW to the University of New England, and he is grateful for the hospitality.

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Authors and Affiliations

  1. School of Science and Technology, University of New England, Armidale, NSW, 2351, Australia

    Yihong Du

  2. Department of Applied Mathematics, National University of Tainan, Tainan, 700, Taiwan

    Chang-Hong Wu

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  1. Yihong Du
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  2. Chang-Hong Wu
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Correspondence to Chang-Hong Wu.

Additional information

Communicated by F. H. Lin.

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Du, Y., Wu, CH. Spreading with two speeds and mass segregation in a diffusive competition system with free boundaries. Calc. Var. 57, 52 (2018). https://doi.org/10.1007/s00526-018-1339-5

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  • DOI: https://doi.org/10.1007/s00526-018-1339-5

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