Stability of the Steady States in Multidimensional Reaction Diffusion Systems Arising in Combustion Theory

Qingxia Li; Xinyao Yang

doi:10.3390/en15218010

Stability of the Steady States in Multidimensional Reaction Diffusion Systems Arising in Combustion Theory

Qingxia Li, Xinyao Yang^*

^*Corresponding author for this work

Department of Applied Mathematics

Fisk University

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

1 Citation (Scopus)

Abstract

We prove that the steady states of a class of multidimensional reaction–diffusion systems are asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, paying particular attention to a special case, namely, systems of equations that arise in combustion theory. The steady-state solutions considered here are the end states of the planar fronts associated with these systems. The present work can be seen as a complement to the previous results on the stability of multidimensional planar fronts.

Original language	English
Article number	8010
Number of pages	22
Journal	Energies
Volume	15
Issue number	21
DOIs	https://doi.org/10.3390/en15218010
Publication status	Published - Oct 2022

Keywords

Planar fronts
Exponential weights
nonlinear stability
steady state

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10.3390/en15218010

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Li, Q., & Yang, X. (2022). Stability of the Steady States in Multidimensional Reaction Diffusion Systems Arising in Combustion Theory. Energies, 15(21), Article 8010. https://doi.org/10.3390/en15218010

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abstract = "We prove that the steady states of a class of multidimensional reaction–diffusion systems are asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, paying particular attention to a special case, namely, systems of equations that arise in combustion theory. The steady-state solutions considered here are the end states of the planar fronts associated with these systems. The present work can be seen as a complement to the previous results on the stability of multidimensional planar fronts.",

keywords = "Planar fronts, Exponential weights, nonlinear stability, steady state",

author = "Qingxia Li and Xinyao Yang",

note = "Funding Information: Research funding was provided by the National Natural Science Foundation of China [Young Scholar 11901468]; Xi{\textquoteright}an Jiaotong-Liverpool University [KSF-E-35]; and the National Science Foundation [NSF-HRD 2112556]. Publisher Copyright: {\textcopyright} 2022 by the authors.",

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doi = "10.3390/en15218010",

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AU - Li, Qingxia

AU - Yang, Xinyao

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]. Publisher Copyright: © 2022 by the authors.

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N2 - We prove that the steady states of a class of multidimensional reaction–diffusion systems are asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, paying particular attention to a special case, namely, systems of equations that arise in combustion theory. The steady-state solutions considered here are the end states of the planar fronts associated with these systems. The present work can be seen as a complement to the previous results on the stability of multidimensional planar fronts.

AB - We prove that the steady states of a class of multidimensional reaction–diffusion systems are asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, paying particular attention to a special case, namely, systems of equations that arise in combustion theory. The steady-state solutions considered here are the end states of the planar fronts associated with these systems. The present work can be seen as a complement to the previous results on the stability of multidimensional planar fronts.

KW - Planar fronts

KW - Exponential weights

KW - nonlinear stability

KW - steady state

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JO - Energies

JF - Energies

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M1 - 8010

ER -

Stability of the Steady States in Multidimensional Reaction Diffusion Systems Arising in Combustion Theory

Abstract

Keywords

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