Abstract
This paper is concerned with the nonlocal dispersal equation
where J is a nonnegative kernel function, the constants λ > 0, δ > 0 and p > 1, the coefficients c(x), q(x) are nonnegative. We investigate the sharp patterns of positive solutions when δ → 0. Our study reveals how the existence of sharp profiles is determined by the behavior of c(x) and q(x). We find that sharp profiles are quite different to the results of classical reaction-diffusion equations.
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Acknowledgments
The author would like to thank the anonymous reviewer for his/her helpful comments. The author also thanks Professors Yihong Du, Wan-Tong Li and Julián López-Gómez for encouragement and useful discussions. This work was partially supported by Fundamental Research Funds for the Central Universities (lzujbky-2021-52).
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Sun, JW. Sharp patterns for some semilinear nonlocal dispersal equations. JAMA 149, 401–419 (2023). https://doi.org/10.1007/s11854-022-0242-3
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DOI: https://doi.org/10.1007/s11854-022-0242-3