@article{337fed559aaf46e7bd02d635da20b469,
title = "Nonlinear stability analysis of stationary solutions for a special class of reaction-diffusion systems with respect to small perturbations",
abstract = "We prove that the stationary solution of a class of reaction-diffusion systems is stable in the intersection of the Sobolev space H1(ℝ) and an exponentially weighted space Hα1(ℝ). Particular attention is given to a special case, the combustion model. The stationary solution considered here is the end state of the traveling front associated with the system, and thus the present result complements recent work by A. Ghazaryan, Y. Latushkin and S. Schecter, where the stability of the traveling fronts was investigated.",
keywords = "Essential spectrum, Exponential weight, Nonlinear stability, Reaction-Diffusion systems, Stationary solutions, Traveling waves",
author = "Qingxia Li and Xinyao Yang and Ziyan Zhang",
note = "Funding Information: Research funding was provided by the National Natural Science Foundation of China [Young Scholar 11901468]; Xi'an Jiaotong-Liverpool University [KSF-E-35]; and the National Science Foundation [NSF-HRD 2112556]. Funding Information: The authors thank Y. Latushkin at the University of Missouri-Columbia, for providing research questions and ideas, and for all the help he gave us. Research funding was provided by the National Natural Science Foundation of China [Young Scholar 11901468]; Xi'an Jiaotong-Liverpool University [KSF-E-35]; and the National Science Foundation [NSF-HRD 2112556]. Publisher Copyright: {\textcopyright} World Scientific and Engineering Academy and Society. All Rights Reserved.",
year = "2022",
month = dec,
doi = "10.37394/23201.2022.21.32",
language = "English",
volume = "21",
pages = "295--305",
journal = "WSEAS Transactions on Circuits and Systems",
issn = "1109-2734",
}