INTERFACE DYNAMICS IN NONLOCAL DISPERSAL FISHER-KPP EQUATIONS

doi:10.1007/s10473-025-0503-1

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (5): 1774-1813.doi: 10.1007/s10473-025-0503-1

INTERFACE DYNAMICS IN NONLOCAL DISPERSAL FISHER-KPP EQUATIONS

Wen TAO, Wantong LI^*, Jianwen SUN, Wenbing XU

1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China;
2. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

收稿日期:2024-03-27 出版日期:2025-09-25 发布日期:2025-10-14

INTERFACE DYNAMICS IN NONLOCAL DISPERSAL FISHER-KPP EQUATIONS

Wen TAO, Wantong LI^*, Jianwen SUN, Wenbing XU

1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China;
2. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

Received:2024-03-27 Online:2025-09-25 Published:2025-10-14
Contact: ^*Wantong Li, E-mail: wtli@lzu.edu.cn
About author:Wen Tao, E-mail: taow18@lzu.edu.cn; Jianwen Sun, jianwensun@lzu.edu.cn; Wenbing Xu, E-mail: 6919@cnu.edu.cn
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).

摘要/Abstract

摘要： 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,

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,

中图分类号:

35F21

Wen TAO, Wantong LI, Jianwen SUN, Wenbing XU. INTERFACE DYNAMICS IN NONLOCAL DISPERSAL FISHER-KPP EQUATIONS[J]. 数学物理学报(英文版), 2025, 45(5): 1774-1813.

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.

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INTERFACE DYNAMICS IN NONLOCAL DISPERSAL FISHER-KPP EQUATIONS

INTERFACE DYNAMICS IN NONLOCAL DISPERSAL FISHER-KPP EQUATIONS

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