Dynamics of the quintic wave equation with nonlocal weak damping

TL;DR

This paper introduces a new analytical scheme to study the long-term behavior of a 3D quintic wave equation with nonlocal weak damping, focusing on attractors and solution dynamics.

Contribution

It provides the first detailed analysis of weak, strong, and exponential attractors for this class of nonlinear wave equations with nonlocal damping.

Findings

Existence of weak, strong, and exponential attractors established.

Analysis of well-posedness and long-time dynamics of the equation.

Insights into nonlinear dissipative evolution with critical nonlinearity.

Abstract

This article presents a new scheme for studying the dynamics of a quintic wave equation with nonlocal weak damping in a 3D smooth bounded domain. As an application, the existence and structure of weak, strong, and exponential attractors for the solution semigroup of this equation are obtained. The investigation sheds light on the well-posedness and long-time behavior of nonlinear dissipative evolution equations with nonlinear damping and critical nonlinearity.