INTERFACE DYNAMICS IN NONLOCAL DISPERSAL FISHER-KPP EQUATIONS

  • Wen TAO ,
  • Wantong LI ,
  • Jianwen SUN ,
  • Wenbing XU
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  • 1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China;
    2. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
Wen Tao, E-mail: taow18@lzu.edu.cn; Jianwen Sun, jianwensun@lzu.edu.cn; Wenbing Xu, E-mail: 6919@cnu.edu.cn

Received date: 2024-03-27

  Online published: 2025-10-14

Supported by

Li's research was partially supported by the NSF of China (12271226), the NSF of Gansu Province of China (21JR7RA537) and the Fundamental Research Funds for the Central Universities (lzujbky-2021-kb15). Sun's research was partially supported by the NSF of China (12371170) and the NSF of Gansu Province of China (21JR7RA535). Xu's research was partially supported by the NSF of China (12201434) and the R&D Program of Beijing Municipal Education Commission (KM202310028017).

Abstract

It is well-known that the propagation phenomena of nonlocal dispersal equations have been extensively studied, and the known results on the interface dynamics of this equation are under the compactly supported initial value. Moreover, there was no explicit formula regarding the interface due to the peculiarity of nonlocal dispersal operators. A natural question is whether it is possible to provide a precise characterization of the interface with respect to small parameter for the general initial values (including exponentially bounded and unbounded). This paper is concerned with the interface dynamics of the nonlocal dispersal equation with scaling parameter. For the exponentially bounded initial value, by choosing the hyperbolic scaling, we show that at a very small time, the interface is confined within a generated layer whose thickness is at most ${O}(\sqrt{\varepsilon}\vert\ln \varepsilon\vert)$, and subsequently, the interface propagates at a linear speed determined by the decay rate of initial value. For a class of exponentially unbounded initial value,

Cite this article

Wen TAO , Wantong LI , Jianwen SUN , Wenbing XU . INTERFACE DYNAMICS IN NONLOCAL DISPERSAL FISHER-KPP EQUATIONS[J]. Acta mathematica scientia, Series B, 2025 , 45(5) : 1774 -1813 . DOI: 10.1007/s10473-025-0503-1

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