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arXiv · 2510.18042

Stabilizing Energy-Critical Wave Equation to a Finite Dimensional Attractor via Nonlinear Damping

Irena Lasiecka·Vando Narciso
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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}.

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Irena Lasiecka, Vando Narciso. 2026-08-26. Stabilizing Energy-Critical Wave Equation to a Finite Dimensional Attractor via Nonlinear Damping. https://arxiv.org/abs/2510.18042

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