In this paper, we study the Gromov-Hausdorff stability and continuous dependence of the inertial manifolds under perturbations of the domain and equation. More precisely, we use the Gromov-Hausdorff distances between two inertial manifolds and two dynamical systems to consider the continuous dependence of the inertial manifolds and the stability of the dynamical systems on inertial manifolds induced by the reaction diffusion equations under perturbations of the domain and equation.

中文翻译：

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惯性流形在域和方程微扰下的 Gromov-Hausdorff 稳定性

在本文中，我们研究了在域和方程的扰动下惯性流形的 Gromov-Hausdorff 稳定性和连续依赖性。更准确地说，我们使用两个惯性流形和两个动力系统之间的 Gromov-Hausdorff 距离来考虑惯性流形的连续依赖性和动力学系统在惯性流形上的稳定性，这些稳定性由域和方程扰动下的反应扩散方程引起.