@article{Pan2024, 
author = {Chaohong Pan and Yan Tang and Hongyong Wang},
title = {Global stability of traveling waves in monostable stream-population model},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {11},
pages = {30745-30760},
keywords = {stream-population model, local stability, global stability, weighted function space, upper and lower solutions},
url = {https://www.sciopen.com/article/10.3934/math.20241485},
doi = {10.3934/math.20241485},
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.}
}