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Dynamics for a Nonlocal Reaction-Diffusion Population Model with a Free Boundary

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Abstract

In this paper we focus on a nonlocal reaction-diffusion population model. Such a model can be used to describe a single species which is diffusing, aggregating, reproducing and competing for space and resources, with the free boundary representing the expanding front. The main objective is to understand the influence of the nonlocal term in the form of an integral convolution on the dynamics of the species. Precisely, when the species successfully spreads into infinity as \(t\rightarrow \infty \), it is proved that the species stabilizes at a positive equilibrium state under rather mild conditions. Furthermore, we obtain a upper bound for the spreading of the expanding front.

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Acknowledgements

The authors would like to express their sincere thanks to the anonymous reviewers for their helpful comments and suggestions. The work is partially supported by PRC grant NSFC 11771380, 11401515.

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Authors and Affiliations

  1. School of Mathematical Science, Yangzhou University, Yangzhou, 225002, China

    Yaling Zhao, Zuhan Liu & Ling Zhou

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  1. Yaling Zhao
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  2. Zuhan Liu
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  3. Ling Zhou
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Correspondence to Ling Zhou.

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Zhao, Y., Liu, Z. & Zhou, L. Dynamics for a Nonlocal Reaction-Diffusion Population Model with a Free Boundary. Acta Appl Math 159, 139–168 (2019). https://doi.org/10.1007/s10440-018-0188-8

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  • DOI: https://doi.org/10.1007/s10440-018-0188-8

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