Asymptotically autonomous stability of kernel sections for lattice plate equations with nonlinear damping

We develop the theory of kernel sections of non-autonomous dynamical systems. Under some sufficient conditions, we establish some abstract results on the asymptotically autonomous stability of kernel sections, which suggests that the time-section of a kernel section is asymptotically stable to a glo...

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Bibliographic Details
Published in:Dynamical systems (London, England) England), 2024-04, Vol.39 (2), p.344-367
Main Authors: Freitas, Mirelson M., Ramos, Anderson J. A., Fonseca, Jociane S.
Format: Article
Language:English
Subjects:
asymptotic autonomy
Asymptotic properties
Attractors (mathematics)
backward compactness
Damping
Kernel sections
lattice plate equations
Mathematical analysis
Primary: 35B40
Secondary: 35B41
Stability
Citations: Items that this one cites
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Summary:We develop the theory of kernel sections of non-autonomous dynamical systems. Under some sufficient conditions, we establish some abstract results on the asymptotically autonomous stability of kernel sections, which suggests that the time-section of a kernel section is asymptotically stable to a global attractor of the autonomous dynamical system. A lattice plate equation with nonlinear damping and non-autonomous forcing is considered as an application. It is shown that the time-section of kernel sections of the non-autonomous lattice plate equations are nonempty, uniformly compact, pullback attracting, and asymptotically stable to a global attractor of the autonomous lattice plate equations.
ISSN:1468-9367
1468-9375
DOI:10.1080/14689367.2024.2307007