Nonlinear stability analysis of stationary solutions for a special class of reaction-diffusion systems with respect to small perturbations

Qingxia Li; Xinyao Yang; Ziyan Zhang

doi:10.37394/23201.2022.21.32

Nonlinear stability analysis of stationary solutions for a special class of reaction-diffusion systems with respect to small perturbations

Qingxia Li
, Xinyao Yang
, Ziyan Zhang

Department of Applied Mathematics

Fisk University

Research output: Contribution to journal › Article › peer-review

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 H_α¹(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.

Original language	English
Pages (from-to)	295-305
Number of pages	11
Journal	WSEAS Transactions on Circuits and Systems
Volume	21
DOIs	https://doi.org/10.37394/23201.2022.21.32
Publication status	Published - Dec 2022

Keywords

Essential spectrum
Exponential weight
Nonlinear stability
Reaction-Diffusion systems
Stationary solutions
Traveling waves

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10.37394/23201.2022.21.32

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@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",

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TY - JOUR

T1 - Nonlinear stability analysis of stationary solutions for a special class of reaction-diffusion systems with respect to small perturbations

AU - Li, Qingxia

AU - Yang, Xinyao

AU - Zhang, Ziyan

N1 - 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: © World Scientific and Engineering Academy and Society. All Rights Reserved.

PY - 2022/12

Y1 - 2022/12

N2 - 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.

AB - 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.

KW - Essential spectrum

KW - Exponential weight

KW - Nonlinear stability

KW - Reaction-Diffusion systems

KW - Stationary solutions

KW - Traveling waves

UR - https://www.scopus.com/pages/publications/85152298290

U2 - 10.37394/23201.2022.21.32

DO - 10.37394/23201.2022.21.32

M3 - Article

AN - SCOPUS:85152298290

SN - 1109-2734

VL - 21

SP - 295

EP - 305

JO - WSEAS Transactions on Circuits and Systems

JF - WSEAS Transactions on Circuits and Systems

ER -

Nonlinear stability analysis of stationary solutions for a special class of reaction-diffusion systems with respect to small perturbations

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Keywords

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