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On the structural monotone inclusion of continuous second-order dynamics combining dry friction and Hessian-driven damping.

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Title: On the structural monotone inclusion of continuous second-order dynamics combining dry friction and Hessian-driven damping.
Authors: Tang, Yan1 (AUTHOR) ttyy7999@163.com, Huang, Yanqin2 (AUTHOR) hyq357821@163.com
Source: Applications of Mathematics. Jun2026, Vol. 71 Issue 3, p299-326. 28p.
Subjects: Dry friction, Dynamical systems, Damping (Mechanics), Monotone operators, Numerical analysis
Abstract: To obtain the null point of the sum for a maximally monotone operator A and a cocoercive operator B, this article is concerned with the asymptotic properties of the trajectories to a second-order continuous damped autonomous dynamical systems with dry friction, which plays a crucial role for achieving stability within a finite time. Additionally, Hessian-driven damping is incorporated, which helps mitigating oscillations for inertial effects. The combination of dry friction and Hessian-driven damping in the context of split monotone inclusions represents a novel contribution, as it simultaneously ensures finite-time convergence and suppresses oscillatory behavior. The existence and uniqueness of global solutions, as well as the convergence of system trajectories are analyzed, the performance of the iterative algorithm generated by the second-order dynamic system discretely are also verified through several numerical experiments. [ABSTRACT FROM AUTHOR]
Copyright of Applications of Mathematics is the property of Springer Nature 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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DbLabel: Engineering Source
An: 195149244
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PubTypeId: academicJournal
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  Data: On the structural monotone inclusion of continuous second-order dynamics combining dry friction and Hessian-driven damping.
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  Data: <searchLink fieldCode="AR" term="%22Tang%2C+Yan%22">Tang, Yan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ttyy7999@163.com</i><br /><searchLink fieldCode="AR" term="%22Huang%2C+Yanqin%22">Huang, Yanqin</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> hyq357821@163.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Applications+of+Mathematics%22">Applications of Mathematics</searchLink>. Jun2026, Vol. 71 Issue 3, p299-326. 28p.
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  Data: <searchLink fieldCode="DE" term="%22Dry+friction%22">Dry friction</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Damping+%28Mechanics%29%22">Damping (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Monotone+operators%22">Monotone operators</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: To obtain the null point of the sum for a maximally monotone operator A and a cocoercive operator B, this article is concerned with the asymptotic properties of the trajectories to a second-order continuous damped autonomous dynamical systems with dry friction, which plays a crucial role for achieving stability within a finite time. Additionally, Hessian-driven damping is incorporated, which helps mitigating oscillations for inertial effects. The combination of dry friction and Hessian-driven damping in the context of split monotone inclusions represents a novel contribution, as it simultaneously ensures finite-time convergence and suppresses oscillatory behavior. The existence and uniqueness of global solutions, as well as the convergence of system trajectories are analyzed, the performance of the iterative algorithm generated by the second-order dynamic system discretely are also verified through several numerical experiments. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Applications of Mathematics is the property of Springer Nature 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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      – Type: doi
        Value: 10.21136/AM.2026.0178-25
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      – Code: eng
        Text: English
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        PageCount: 28
        StartPage: 299
    Subjects:
      – SubjectFull: Dry friction
        Type: general
      – SubjectFull: Dynamical systems
        Type: general
      – SubjectFull: Damping (Mechanics)
        Type: general
      – SubjectFull: Monotone operators
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
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      – TitleFull: On the structural monotone inclusion of continuous second-order dynamics combining dry friction and Hessian-driven damping.
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            NameFull: Tang, Yan
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              M: 06
              Text: Jun2026
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              Y: 2026
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              Value: 71
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