一类具有时滞的反应扩散Lotka-Volterra合作系统行波解的存在性
Existence of Traveling Wave Solution for Reaction-Diffusion Lotka-Volterra Cooperative System with Time Delay
摘要: 本文研究了移动环境下一类具有时滞的Lotka-Volterra合作系统行波解的存在性。利用单调迭代方法，通过构造合适的上下解，证明了当环境运动速度 c>max{ c 1 ∗ , c 2 ∗ } 时，系统连接两边界平衡点的行波解的存在性。
Abstract: Existence of traveling wave front solutions is established for diffusive and cooperative Lotka-Volterra system with delays in a shifting environment. Using the method of monotone iteration and by constructing appropriate upper and lower solutions, it is proven that when the environmental movement speed is c>max{ c 1 ∗ , c 2 ∗ } , there exist traveling wave solutions that connect the boundary equilibrium points of the system.
文章引用：张贝贝. 一类具有时滞的反应扩散Lotka-Volterra合作系统行波解的存在性[J]. 应用数学进展, 2024, 13(8): 4034-4042. https://doi.org/10.12677/aam.2024.138384

参考文献

[1] Fisher, R.A. (1937) The Wave of Advance of Advantageous Genes. Annals of Eugenics, 7, 355-369. [Google Scholar] [CrossRef] 
[2] Kolomgorov, A.N., Petrovskii, I.G. and Piskunov, N.S. (1937) Study of a Diffusion Equation That Is Related to the Growth of a Quality of Matter, and Its Application to a Biological Problem. Moscow University Mathematics Bulletin, 1, 1-26.
[3] Nakata, Y. and Muroya, Y. (2010) Permanence for Nonautonomous Lotka-Volterra Cooperative Systems with Delays. Nonlinear Analysis: Real World Applications, 11, 528-534. [Google Scholar] [CrossRef] 
[4] Lotka, A.J. (1925) Elements of Physical Biology. Williams & Wilkins Company.
[5] Volterra, V. (1928) Variations and Fluctuations of the Number of Individuals in Animal Species Living Together. ICES Journal of Marine Science, 3, 3-51. [Google Scholar] [CrossRef] 
[6] Li, B., Weinberger, H.F. and Lewis, M.A. (2005) Spreading Speeds as Slowest Wave Speeds for Cooperative Systems. Mathematical Biosciences, 196, 82-98. [Google Scholar] [CrossRef] [PubMed]
[7] Li, L. and Ghoreishi, A. (1991) On Positive Solutions of General Nonlinear Elliptic Symbiotic Interacting Systems. Applicable Analysis, 40, 281-295. [Google Scholar] [CrossRef] 
[8] Lou, Y. (1996) Necessary and Sufficient Condition for the Existence of Positive Solutions of Certain Cooperative System. Nonlinear Analysis: Theory, Methods & Applications, 26, 1079-1095. [Google Scholar] [CrossRef] 
[9] Wang, Z. and Han, B. (2016) Traveling Wave Solutions in a Nonlocal Reaction-Diffusion Population Model. Communications on Pure and Applied Analysis, 15, 1057-1076. [Google Scholar] [CrossRef] 
[10] Han, B. and Yang, Y. (2017) On a Predator-Prey Reaction-Diffusion Model with Nonlocal Effects. Communications in Nonlinear Science and Numerical Simulation, 46, 49-61. [Google Scholar] [CrossRef] 
[11] Troy, W.C. (1980) The Existence of Traveling Wave Front Solutions of a Model of the Belousov-Zhabotinskii Chemical Reaction. Journal of Differential Equations, 36, 89-98. [Google Scholar] [CrossRef] 
[12] Li, K. and Li, X. (2012) Traveling Wave Solutions in a Delayed Diffusive Competition System. Nonlinear Analysis: Theory, Methods & Applications, 75, 3705-3722. [Google Scholar] [CrossRef] 
[13] Yang, Y., Wu, C. and Li, Z. (2019) Forced Waves and Their Asymptotics in a Lotka-Volterra Cooperative Model under Climate Change. Applied Mathematics and Computation, 353, 254-264. [Google Scholar] [CrossRef] 
[14] Wang, H., Pan, C. and Ou, C. (2020) Existence of Forced Waves and Gap Formations for the Lattice Lotka-Volterra Competition System in a Shifting Environment. Applied Mathematics Letters, 106, Article 106349. [Google Scholar] [CrossRef] 
[15] Wu, C. and Xu, Z. (2021) Propagation Dynamics in a Heterogeneous Reaction-Diffusion System under a Shifting Environment. Journal of Dynamics and Differential Equations, 35, 493-521. [Google Scholar] [CrossRef] 
[16] Wang, H., Pan, C. and Ou, C. (2021) Existence, Uniqueness and Stability of Forced Waves to the Lotka-Volterra Competition System in a Shifting Environment. Studies in Applied Mathematics, 148, 186-218. [Google Scholar] [CrossRef] 

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