Dynamics of the quintic wave equation with nonlocal weak damping

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.

44 pages,1 figure