Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 84, pp. 1-25.

Title: Asymptotic behavior of Kirchhoff type plate equations with nonlocal weak damping, anti-damping and subcritical nonlinearity

Authors: Ling Xu (Northwest Normal Univ., Lanzhou, Gansu, China)
         Yanni Wang (Northwest Normal Univ., Lanzhou, Gansu, China)
         Bianxia Yang (Northwest A and F Univ., Yangling, Shaanxi, China)

Abstract:
In this work we study the global well-posedness, dissipativity and existence of
global attractors for Kirchhoff type plate equations with nonlocal weak damping and
anti-damping, when the nonlinear term $g(u)$ satisfies a subcritical growth condition.
Firstly, we show the global well-posedness of this system by the monotone operator
theory with locally Lipschitz perturbation.
Secondly, we construct a refined Gronwall's inequality and then apply the barrier
method to prove the dissipativity for this system. Lastly, the asymptotic smoothness
by taking advantage of the energy reconstruction method, we deduce the existence of
a global attractor for this system.

Submitted February 7, 2025. Published August 11, 2025.
Math Subject Classifications: 35B40, 35B41, 35Q35.
Key Words: Plate equation; nonlocal weak damping; anti-damping.