Existence of the global attractor for the plate equation with nonlocal nonlinearity in R^{n}

TL;DR

This paper proves the existence of a global attractor for a semilinear plate equation with nonlocal nonlinearity in R^n, under mild damping conditions, contributing to the understanding of long-term behavior of such systems.

Contribution

It establishes the existence of a global attractor for the plate equation with nonlocal nonlinearity, a novel result in this context.

Findings

Global attractor exists for the semilinear plate equation

Results hold under mild damping conditions

Advances understanding of long-term dynamics in nonlocal PDEs

Abstract

We consider Cauchy problem for the semilinear plate equation with nonlocal nonlinearity. Under mild conditions on the damping coefficient, we prove that the semigroup generated by this problem possesses a global attractor.