ENTIRE SOLUTIONS OF LOTKA-VOLTERRA COMPETITION SYSTEMS WITH NONLOCAL DISPERSAL*

doi:10.1007/s10473-023-0602-9

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (6): 2347-2376.doi: 10.1007/s10473-023-0602-9

ENTIRE SOLUTIONS OF LOTKA-VOLTERRA COMPETITION SYSTEMS WITH NONLOCAL DISPERSAL^*

Yuxia HAO^1,2, Wantong LI^1,†, Jiabing WANG³, Wenbing XU⁴

1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China;
2. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China;
3. School of Mathematics and Physics, Center for Mathematical Sciences, China University of Geosciences, Wuhan 430074, China;
4. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

收稿日期:2022-04-05 修回日期:2023-05-22 发布日期:2023-12-08
通讯作者: †Wantong LI, E-mail: wtli@lzu.edu.cn
作者简介:Yuxia HAO, E-mail: haoyx15@lzu.edu.cn; Jiabing WANG, E-mail: wangjb@cug.edu.cn; Wenbing XU, E-mail: 6919@cnu.edu.cn
基金资助:
Research of W.-T. Li 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-2022-sp07); research of J.-B. Wang was partially supported by the Basic and Applied Basic Research Foundation of Guangdong Province (2023A1515011757) and the National Natural Science Foundation of China (12271494), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (G1323523061) and research of W.-B. Xu was partially supported by the NSF of China (12201434).

ENTIRE SOLUTIONS OF LOTKA-VOLTERRA COMPETITION SYSTEMS WITH NONLOCAL DISPERSAL^*

Yuxia HAO^1,2, Wantong LI^1,†, Jiabing WANG³, Wenbing XU⁴

1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China;
2. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China;
3. School of Mathematics and Physics, Center for Mathematical Sciences, China University of Geosciences, Wuhan 430074, China;
4. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

Received:2022-04-05 Revised:2023-05-22 Published:2023-12-08
Contact: †Wantong LI, E-mail: wtli@lzu.edu.cn
About author:Yuxia HAO, E-mail: haoyx15@lzu.edu.cn; Jiabing WANG, E-mail: wangjb@cug.edu.cn; Wenbing XU, E-mail: 6919@cnu.edu.cn
Supported by:
Research of W.-T. Li 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-2022-sp07); research of J.-B. Wang was partially supported by the Basic and Applied Basic Research Foundation of Guangdong Province (2023A1515011757) and the National Natural Science Foundation of China (12271494), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (G1323523061) and research of W.-B. Xu was partially supported by the NSF of China (12201434).

摘要/Abstract

摘要： This paper is mainly concerned with entire solutions of the following two-species Lotka-Volterra competition system with nonlocal (convolution) dispersals:Here $a\neq 1$, $b\neq1$, $d$, and $r$ are positive constants. By studying the eigenvalue problem of (0.1) linearized at $(\phi_c(\xi), 0)$, we construct a pair of super- and sub-solutions for (0.1), and then establish the existence of entire solutions originating from $(\phi_c(\xi), 0)$ as $t\rightarrow -\infty$, where $\phi_c$ denotes the traveling wave solution of the nonlocal Fisher-KPP equation $u_t=k*u-u+u\left(1-u\right)$. Moreover, we give a detailed description on the long-time behavior of such entire solutions as $t\rightarrow \infty$. Compared to the known works on the Lotka-Volterra competition system with classical diffusions, this paper overcomes many difficulties due to the appearance of nonlocal dispersal operators.

关键词: entire solutions, Lotka-Volterra competition systems, nonlocal dispersal, traveling waves

Abstract: This paper is mainly concerned with entire solutions of the following two-species Lotka-Volterra competition system with nonlocal (convolution) dispersals:Here $a\neq 1$, $b\neq1$, $d$, and $r$ are positive constants. By studying the eigenvalue problem of (0.1) linearized at $(\phi_c(\xi), 0)$, we construct a pair of super- and sub-solutions for (0.1), and then establish the existence of entire solutions originating from $(\phi_c(\xi), 0)$ as $t\rightarrow -\infty$, where $\phi_c$ denotes the traveling wave solution of the nonlocal Fisher-KPP equation $u_t=k*u-u+u\left(1-u\right)$. Moreover, we give a detailed description on the long-time behavior of such entire solutions as $t\rightarrow \infty$. Compared to the known works on the Lotka-Volterra competition system with classical diffusions, this paper overcomes many difficulties due to the appearance of nonlocal dispersal operators.

Key words: entire solutions, Lotka-Volterra competition systems, nonlocal dispersal, traveling waves

中图分类号:

35K57

Yuxia HAO, Wantong LI, Jiabing WANG, Wenbing XU. ENTIRE SOLUTIONS OF LOTKA-VOLTERRA COMPETITION SYSTEMS WITH NONLOCAL DISPERSAL^*[J]. 数学物理学报(英文版), 2023, 43(6): 2347-2376.

Yuxia HAO, Wantong LI, Jiabing WANG, Wenbing XU. ENTIRE SOLUTIONS OF LOTKA-VOLTERRA COMPETITION SYSTEMS WITH NONLOCAL DISPERSAL^*[J]. Acta mathematica scientia,Series B, 2023, 43(6): 2347-2376.

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ENTIRE SOLUTIONS OF LOTKA-VOLTERRA COMPETITION SYSTEMS WITH NONLOCAL DISPERSAL^*

ENTIRE SOLUTIONS OF LOTKA-VOLTERRA COMPETITION SYSTEMS WITH NONLOCAL DISPERSAL^*

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