Gromov-Hausdorff stability of global attractors of damped wave equations under perturbations of the domain
Ngoctu Bui, Jihoon Lee
TL;DR
This paper demonstrates that the global attractors of damped wave equations remain stable under domain perturbations by employing the Gromov-Hausdorff distance, ensuring continuous dependence on domain shape.
Contribution
It introduces a novel approach using Gromov-Hausdorff distance to analyze the stability of attractors under domain perturbations for damped wave equations.
Findings
Global attractors depend continuously on domain shape
Gromov-Hausdorff distance measures stability effectively
Attractors exhibit stability under small domain perturbations
Abstract
In this paper, we will make use of the Gromov-Hausdorff distance between compact metric spaces to establish the continuous dependence and the Gromov-Hausdorff stability of global attractors for damped wave equations under perturbations of the domain.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Nonlinear Differential Equations Analysis · Advanced Mathematical Physics Problems