Global stability of traveling waves in monostable stream-population model

Chaohong Pan; Yan Tang; Hongyong Wang; Chaohong Pan; Yan Tang; Hongyong Wang

doi:10.3934/math.20241485

AIMS Mathematics

2024, Volume 9, Issue 11: 30745-30760. doi: 10.3934/math.20241485

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Global stability of traveling waves in monostable stream-population model

1.
School of Mathematics and Statistics, Hunan First Normal University, Changsha 421205, China
2.
School of Mathematics and Physics, University of South China, Hengyang 421001, China

Received: 10 August 2024 Revised: 10 October 2024 Accepted: 14 October 2024 Published: 30 October 2024
MSC : 35B35, 35B40, 35B51, 37C65, 92D25

The stability of monotone traveling waves to a stream-population model is established in a particular weighted function space via the method of upper and lower solutions and a squeezing technique. By analyzing the behaviors of the traveling wave for a large time period under a small perturbation, we obtain the results of the local stability. The comparison principle and the squeeze theorem also allows us to prove the global stability of the positive steady-state solutions in the special weighted function space by constructing suitable upper and lower solutions.
- stream-population model,
- local stability,
- global stability,
- weighted function space,
- upper and lower solutions
Citation: Chaohong Pan, Yan Tang, Hongyong Wang. Global stability of traveling waves in monostable stream-population model[J]. AIMS Mathematics, 2024, 9(11): 30745-30760. doi: 10.3934/math.20241485

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Abstract

The stability of monotone traveling waves to a stream-population model is established in a particular weighted function space via the method of upper and lower solutions and a squeezing technique. By analyzing the behaviors of the traveling wave for a large time period under a small perturbation, we obtain the results of the local stability. The comparison principle and the squeeze theorem also allows us to prove the global stability of the positive steady-state solutions in the special weighted function space by constructing suitable upper and lower solutions.

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