Global attractors for the plate equation with nonlocal nonlinearity in unbounded domains

TL;DR

This paper investigates the long-term behavior of solutions to a semilinear plate equation with nonlocal nonlinearity in unbounded domains, proving the existence, regularity, and finite dimensionality of its global attractor.

Contribution

It establishes the existence and detailed properties of a global attractor for the plate equation with nonlocal nonlinearity in unbounded domains, which was previously unaddressed.

Findings

Existence of a global attractor

Regularity of the attractor

Finite dimensionality of the attractor

Abstract

We consider the initial value problem for the semilinear plate equation with nonlocal nonlinearity. We prove the existence of global attractor and then establish the regularity and finite dimensionality of this attractor.