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Structural stability for scalar reaction-diffusion equations
- Source :
- Electronic Journal of Qualitative Theory of Differential Equations, Vol 2023, Iss 54, Pp 1-12 (2023)
- Publication Year :
- 2023
- Publisher :
- University of Szeged, 2023.
-
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.
Details
- Language :
- English
- ISSN :
- 14173875
- Volume :
- 2023
- Issue :
- 54
- Database :
- Directory of Open Access Journals
- Journal :
- Electronic Journal of Qualitative Theory of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.43428b0addb4c0ebc63150b5f8b9efd
- Document Type :
- article
- Full Text :
- https://doi.org/10.14232/ejqtde.2023.1.54