Asymptotic behaviour of the wave equation with nonlocal weak damping, anti-damping and critical nonlinearity

TL;DR

This paper investigates the long-term behavior of a wave equation influenced by nonlocal damping and anti-damping effects, along with critical nonlinearities, establishing the existence of a global attractor.

Contribution

It proves the existence of a global attractor for the wave equation with complex nonlocal damping, anti-damping, and critical nonlinearities, advancing understanding of such systems.

Findings

Existence of a global attractor established

Analysis of wave equations with nonlocal effects

Insights into long-term dynamics of nonlinear wave systems

Abstract

In this paper we prove the existence of the global attractor for the wave equation with nonlocal weak damping, nonlocal anti-damping and critical nonlinearity.