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

Abstract

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.

Keywords:

• Kernel sections
• backward compactness
• asymptotic autonomy
• lattice plate equations

2010 Mathematics Subject Classifications:

• Primary: 35B40
• Secondary: 35B41
• 37L30

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

This article describes entirely theoretical research. There is no data involved in this research.

Additional information

Funding

M. M. Freitas has been supported by CNPq [grant number 313081/2021-2]. A. J. A. Ramos has been supported by CNPq [grant number 305848/2022-4].