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Approximation Solutions of Some Nonlocal Dispersal Problems

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Abstract

This paper is concerned with a class of nonlocal dispersal problem with Dirichlet boundary conditions. We analyze the limit of solutions when the dispersal kernel is rescaled. Our main results reveal that the solutions of Dirichlet heat equation can be approximated by the nonlocal dispersal equation. The investigation also shows that the nonlocal dispersal equation is similar to the convection–diffusion equation by taking another special kernel function.

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Acknowledgements

J.W. Sun would like to thank Professor Wenxian Shen for useful discussions. This work was supported by NSF of China (11401277,11731005), NSF of Gansu Province (21JR7RA535,21JR7RA537) and Fundamental Research Funds for the Central Universities (lzujbky-2021-52).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Yaping Du & Jian-Wen Sun

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  1. Yaping Du
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  2. Jian-Wen Sun
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Correspondence to Jian-Wen Sun.

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Communicated by Syakila Ahmad.

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Du, Y., Sun, JW. Approximation Solutions of Some Nonlocal Dispersal Problems. Bull. Malays. Math. Sci. Soc. 46, 8 (2023). https://doi.org/10.1007/s40840-022-01403-z

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  • DOI: https://doi.org/10.1007/s40840-022-01403-z

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