Gromov-Hausdorff stability for semilinear systems with large diffusion
DOI:
https://doi.org/10.12775/TMNA.2023.034Keywords
Gromov-Hausdorff stability, global attractors, large diffusivity, reaction-diffusion equationsAbstract
This paper deals with the Gromov-Hausdorff stability for systems generated of reaction-diffusion equations whose diffusion coefficients are simultaneously large in a bounded smooth domains. The appropriated framework is presented to establish the conjugation between the attractors by means o f $\varepsilon$-isometries.References
A. Arbieto and C. Morales, Topological stability from Gromov–Hausdorff viewpoint, Discrete Contin. Dyn. Syst. 37 (2017), 3531–3544.
J.M. Arrieta and A.N. Carvalho, Spectral convergence and nonlinear dynamics of reaction-diffusion equations under perturbations of the domain, J. Differential Equations 199 (2004), 143–178.
J.M. Arrieta, A.N. Carvalho and A. Rodrı́guez-Bernal, Attractors for parabolic problems with nonlinear boundary bondition. Uniform bounds, Comm. Partial Differential Equations 25 (2000), 1–37.
A.N. Carvalho and L. Pires, Rate of convergence of attractors for singularly perturbed semilinear problems, J. Math. Anal. Appl. 452 (2017), 258–296.
A.N. Carvalho and L. Pires, Parabolic equations with localized large diffusion: rate of convergence of attractors, Topol. Methods Nonlinear Anal. 53 (2019), 1–23.
A.N. Carvalho and M.R. Primo, Spatial homogeneity in parabolic problems with nonlinear boundary conditions, Commun. Pure Appl. Anal. 3 (2004), 637–651.
M. Gromov, Metric Structures for Riemannian and Non-Riemannian Spaces, Birkhäuser, Basel, 2007.
J.K. Hale, Large diffusivity and asymptotic behavior in parabolic systems, J. Math. Anal. Appl. 118 (1986), 455–466.
J.K. Hale and C. Rocha, Varying boundary conditions with large diffusion, J. Math. Pures Appl. 66 (1987), 139–158.
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol. 840, Springer–Velag, 1980.
J. Lee, Gromov–Hausdorff stability of reaction diffusion equations with Neumann boundary conditions under perturbations of the domain, J. Math. Anal. Appl. 496 (2021), 1–18.
J. Lee and N. Nguyen, Topological stability of Chafee–Infante equation under Lipischitz perturbations of the domain and equation, J. Math. Anal. Appl. 517 (2023), 126628.
J. Lee, N. Nguyen and V.M. Toi, Gromov–Hausdorff stability of global attractors of reaction diffusion equations under perturbations of domain, J. Differential Equations 239 (2020), 125–147.
J. Lee and N.T. Nguyen, Gromov–Hausdorff stability of reaction diffusion equations with Robin boundary conditions under perturbations of the domain and equation, Commun. Pure Appl. Anal. 20 (2021), 1263–1296.
L. Pires and R.A. Samprogna, Rate of convergence of global attractors for some perturbed reaction-diffusion equations under smooth perturbations of the domain, Topol. Methods Nonlinear Anal. 58 (2021), 441–452.
R. Willie, A semilinear reaction-diffusion system of equations and large diffusion, J. Dynam. Differential Equations 16 (2004), 35–63.
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Copyright (c) 2024 Jihoon Lee, Ngocthach Nguyen, Leonardo Pires
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