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Traveling Waves for a Sign-Changing Nonlocal Evolution Equation with Delayed Nonlocal Response

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Abstract

This paper deals with the existence of traveling wave solutions for a nonlocal evolution equation with delayed nonlocal response and sign-changing kernel. By constructing a new pair of upper-lower solutions and applying Schauder’s fixed point theorem, we first prove that there exists a number \(c^{\#}>0\) such that when \(c>c^{\#}\), the nonlocal evolution equation admits a semi-wave solution with wave speed c, which connects the trivial equilibrium 0 at negative infinity. Then, we analyze the asymptotic behavior of wave profile at positive infinity and obtain the existence of a traveling wave solution with speed c and connecting the trivial equilibrium 0 and the positive equilibrium 1, when the wave speed c is large.

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Acknowledgements

This research was partially supported by NSF of China [12261081] and NSF of Gansu Province [21JR7RA121]. The first author is supported by 2022 Gansu Province Excellent Graduate Student “Innovation Star” Project (2022CXZX-239).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, Gansu, China

    Juan He & Guo-Bao Zhang

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  1. Juan He
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  2. Guo-Bao Zhang
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Correspondence to Guo-Bao Zhang.

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Communicated by Shangjiang Guo.

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He, J., Zhang, GB. Traveling Waves for a Sign-Changing Nonlocal Evolution Equation with Delayed Nonlocal Response. Bull. Malays. Math. Sci. Soc. 47, 42 (2024). https://doi.org/10.1007/s40840-023-01638-4

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  • DOI: https://doi.org/10.1007/s40840-023-01638-4

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