Affiliation:
1. Chonnam National University
2. State University of Ponta Grossa
Abstract
In this paper, we prove the structural stability for a family of
scalar reaction-diffusion equations. Our arguments consist of using
invariant manifold theorem to reduce the problem to a finite dimension and
then, we use the structural stability of Morse–Smale flows in a finite
dimension to obtain the corresponding result in infinite dimension. As a
consequence, we obtain the optimal rate of convergence of the attractors
and estimate the Gromov–Hausdorff distance of the attractors using
continuous $\varepsilon$-isometries.