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Wavefronts of a Nonlocal State-dependent Time Delay Model

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Abstract

This paper is concerned with the travelling wavefronts of a nonlocal dispersal cooperation model with harvesting and state-dependent delay, which is assumed to be an increasing function of the population density with lower and upper bound. Especially, state-dependent delay is introduced into a nonlocal reaction-diffusion model. The conditions of Schauder’s fixed point theorem are proved by constructing a reasonable set of functions Γ (see Section 2) and a pair of upper-lower solutions, so the existence of traveling wavefronts is established. The present study is continuation of a previous work that highlights the Laplacian diffusion.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, 233030, P. R. China

    Rui Jun Xie & Zhi Hui Yang

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China

    Rong Yuan

Authors
  1. Rui Jun Xie
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  2. Rong Yuan
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  3. Zhi Hui Yang
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Correspondence to Rui Jun Xie.

Additional information

Supported by NSFC (Grant Nos. 11771044, 11871007) and Foundation of Anhui University of Finance and Economics (Grant No. ACKYC19051), Major Research Projects of Natural Science in Colleges and Universities of Anhui Province (Grant No. KJ2017ZD35)

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Xie, R.J., Yuan, R. & Yang, Z.H. Wavefronts of a Nonlocal State-dependent Time Delay Model. Acta. Math. Sin.-English Ser. 36, 77–92 (2020). https://doi.org/10.1007/s10114-019-8400-y

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  • DOI: https://doi.org/10.1007/s10114-019-8400-y

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