Abstract / Introduction

In this paper, we study the dynamics of nonlinear parabolic equations under Lipschitz perturbations of the domain and equation. We first prove the continuity of global attractors of the equations obtained by Lipschitz perturbations of a given equation, which generalize Theorems 4.1 and 4.2 in [12]. Using this fact, we show that the dynamical system induced by a reaction diffusion equation is Gromov-Hausdorff stable on its global attractor if its equilibrium points are hyperbolic.