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Propagation Phenomena for a Lotka–Volterra Cooperative Model with Degenerate Diffusion Under Climate Change

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Abstract

This paper is concerned with a Lotka–Volterra cooperative model with degenerate diffusion under climate change. Firstly, by constructing the appropriate upper and lower solutions to overcome the influence of the degeneracy and nonautonomous terms, and applying the monotone iteration method, we prove the existence of forced traveling waves with any speed \(c>0\) at which the habitat edge is shifting. Then based on the new comparison theorem for degenerate diffusion systems, we obtain the global existence of \(C^{\alpha ,\beta }\)-solution to the initial value problem of this system via the compactness analysis. At the end of the paper, some numerical simulations are conducted.

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Acknowledgements

Rui Yan’s research is supported by Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province (20230030). Guirong Liu’s research is supported by the National Natural Science Foundation of China (no. 11971279). Yuzhe Qin’s research is supported by the National Natural Science Foundation of China (no. 12201369). Yang Wang’s research is supported in part by the National Natural Science Foundation of China (no. 11901366), Shanxi Scholarship Council of China (2021-001) and Fundamental Research Program of Shanxi Province (no. 202303021221069).

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Authors and Affiliations

  1. School of Applied Mathematics, Shanxi University of Finance and Economics, 030006, Taiyuan, China

    Rui Yan

  2. School of Mathematical Sciences, Shanxi University, 030006, Taiyuan, China

    Guirong Liu, Yuzhe Qin & Yang Wang

  3. Key Laboratory of Complex Systems and Data Science of Ministry of Education, Shanxi University, 030006, Taiyuan, China

    Guirong Liu, Yuzhe Qin & Yang Wang

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  1. Rui Yan
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Rui Yan, Guirong Liu and Yang Wang wrote the main manuscript text and Yuzhe Qin prepared figures in this manuscript. All authors reviewed the manuscript.

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Correspondence to Yang Wang.

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Yan, R., Liu, G., Qin, Y. et al. Propagation Phenomena for a Lotka–Volterra Cooperative Model with Degenerate Diffusion Under Climate Change. Qual. Theory Dyn. Syst. 23, 155 (2024). https://doi.org/10.1007/s12346-024-01015-x

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