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BOUNDARY STABILIZATION OF A CLASS OF COUPLED REACTION-DIFFUSION SYSTEM WITH ONE CONTROL.

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Titel: BOUNDARY STABILIZATION OF A CLASS OF COUPLED REACTION-DIFFUSION SYSTEM WITH ONE CONTROL.
Autoren: ARIAS, GONZALO1 ngonzaloandres@uc.cl, PARADA, HUGO2 hugo.parada@math.univ-toulouse.fr
Quelle: SIAM Journal on Control & Optimization. 2025, Vol. 63 Issue 4, p2783-2808. 26p.
Schlagwörter: *CONTROL theory (Engineering), BACKSTEPPING control method, SINGULAR perturbations, DIFFUSION coefficients, STABILITY theory, REACTION-diffusion equations, EIGENVALUES
Abstract: Controllability and stabilization of coupled reaction-diffusion systems has been widely studied in the last few decades. In recent years, coupling reaction-diffusion systems to elliptic equations has been gaining attention. These systems arise as a simplified model for coupled reactiondiffusion systems when at least one diffusion coefficient is high. In this article, we study the eigenvalues of a coupled reaction-diffusion system with one high diffusion. As a consequence, when this system is unstable we are able to build a Backstepping-based controller to stabilize it. This is achieved due to the singular perturbation method (SPM), which provides a methodology to study the behavior of the eigenvalues with respect to the singular perturbation parameter. Additionally, the SPM helps in building controller based on the reduced models, which are used to stabilize the coupled system when one diffusion is high enough. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Control & Optimization is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: BOUNDARY STABILIZATION OF A CLASS OF COUPLED REACTION-DIFFUSION SYSTEM WITH ONE CONTROL.
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  Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Control+%26+Optimization%22">SIAM Journal on Control & Optimization</searchLink>. 2025, Vol. 63 Issue 4, p2783-2808. 26p.
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  Data: *<searchLink fieldCode="DE" term="%22CONTROL+theory+%28Engineering%29%22">CONTROL theory (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22BACKSTEPPING+control+method%22">BACKSTEPPING control method</searchLink><br /><searchLink fieldCode="DE" term="%22SINGULAR+perturbations%22">SINGULAR perturbations</searchLink><br /><searchLink fieldCode="DE" term="%22DIFFUSION+coefficients%22">DIFFUSION coefficients</searchLink><br /><searchLink fieldCode="DE" term="%22STABILITY+theory%22">STABILITY theory</searchLink><br /><searchLink fieldCode="DE" term="%22REACTION-diffusion+equations%22">REACTION-diffusion equations</searchLink><br /><searchLink fieldCode="DE" term="%22EIGENVALUES%22">EIGENVALUES</searchLink>
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  Label: Abstract
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  Data: Controllability and stabilization of coupled reaction-diffusion systems has been widely studied in the last few decades. In recent years, coupling reaction-diffusion systems to elliptic equations has been gaining attention. These systems arise as a simplified model for coupled reactiondiffusion systems when at least one diffusion coefficient is high. In this article, we study the eigenvalues of a coupled reaction-diffusion system with one high diffusion. As a consequence, when this system is unstable we are able to build a Backstepping-based controller to stabilize it. This is achieved due to the singular perturbation method (SPM), which provides a methodology to study the behavior of the eigenvalues with respect to the singular perturbation parameter. Additionally, the SPM helps in building controller based on the reduced models, which are used to stabilize the coupled system when one diffusion is high enough. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of SIAM Journal on Control & Optimization is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1137/24M1656311
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 26
        StartPage: 2783
    Subjects:
      – SubjectFull: CONTROL theory (Engineering)
        Type: general
      – SubjectFull: BACKSTEPPING control method
        Type: general
      – SubjectFull: SINGULAR perturbations
        Type: general
      – SubjectFull: DIFFUSION coefficients
        Type: general
      – SubjectFull: STABILITY theory
        Type: general
      – SubjectFull: REACTION-diffusion equations
        Type: general
      – SubjectFull: EIGENVALUES
        Type: general
    Titles:
      – TitleFull: BOUNDARY STABILIZATION OF A CLASS OF COUPLED REACTION-DIFFUSION SYSTEM WITH ONE CONTROL.
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            NameFull: ARIAS, GONZALO
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          Name:
            NameFull: PARADA, HUGO
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          Dates:
            – D: 01
              M: 07
              Text: 2025
              Type: published
              Y: 2025
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              Value: 63
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              Value: 4
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            – TitleFull: SIAM Journal on Control & Optimization
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