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Long-Time Behavior of a Reaction–Diffusion Model with Strong Allee Effect and Free Boundary: Effect of Protection Zone

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Abstract

This paper concerns the effect of the (separated/connected) protection zone for the evolution of an endangered species on the reaction–diffusion equation with the strong Allee effect and the free boundary. First, we describe the long-time dynamical behavior of the system of two types protection zones with the same length. Furthermore, the asymptotic profiles of solutions and the asymptotic spreading speed are estimated when spreading happens. Our results, together with those in previous papers Du et al. (J Differ Equ 266:7327–7356, 2019), Du and Lou (J Eur Math Soc 17:2673–2724, 2015) on two other closely related models, show that the protection zone and the free boundary play an important role in the evolution of the endangered species.

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Acknowledgements

We would like to express our thanks to Prof. Rui Peng for his kind encouragements and valuable suggestions during the preparation of this work. We also thank the reviewer for his/her careful reading and useful suggestions which lead to an improvement of the presentation.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, Shandong Province, China

    Ningkui Sun

  2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu Province, China

    Chengxia Lei

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  1. Ningkui Sun
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  2. Chengxia Lei
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Correspondence to Chengxia Lei.

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N. Sun was partially supported by NSF of China (No. 11801330), the Higher Educational Science and Technology Program of Shandong Province (No. J18KA226), and C. Lei was partially supported by NSF of China (No. 11971454, 11801232), the Priority Academic Program Development of Jiangsu Higher Education Institution, the Natural Science Foundation of the Jiangsu Province (No. BK20180999), the Foundation of Jiangsu Normal University (No. 17XLR008)

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Sun, N., Lei, C. Long-Time Behavior of a Reaction–Diffusion Model with Strong Allee Effect and Free Boundary: Effect of Protection Zone. J Dyn Diff Equat 35, 737–770 (2023). https://doi.org/10.1007/s10884-021-10027-z

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  • DOI: https://doi.org/10.1007/s10884-021-10027-z

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