Stabilizing Energy-Critical Wave Equation to a Finite Dimensional Attractor via Nonlinear Damping
Abstract
The wave equation with energy critical sources and nonlinear damping defined on a 3D bounded domain is considered. It is shown that the resulting dynamical system admits a global attractor. Under the additional assumption of strong monotonicity of the damping at the origin, it is shown that the originally unstable quintic wave is uniformly stabilised to a finite dimensional and smooth set. Moreover, the existence of exponential attractor is established. In order to handle \enquote{energy criticality} of both sources and damping, the methods used depend on enhanced dissipation \cite{Bociu-lasiecka-jde}, energy {\it identity} for weak solutions \cite{Koch-lasiecka}, an adaptation of Ball's method \cite{ball}, and the theory of quasi-stable systems \cite{chueshov-white}.
Cite
@article{arxiv.2510.18042,
title = {Stabilizing Energy-Critical Wave Equation to a Finite Dimensional Attractor via Nonlinear Damping},
author = {Irena Lasiecka and Vando Narciso},
journal= {arXiv preprint arXiv:2510.18042},
year = {2025}
}