Rate of convergence of global attractors for some perturbed reaction-diffusion equations under smooth perturbations of the domain
DOI:
https://doi.org/10.12775/TMNA.2020.074Keywords
Attractors, domain perturbation, rate of attraction, reaction diffusion equationsAbstract
In this paper we obtain a rate of convergence for the asymptotic behavior of some semilinar parabolic problems with Dirichlet boundary conditions relatively to smooth perturbations of the domain. We will obtain a rate of convergence dependent on convergence of domains for eigenvalues, eigenfunctions, invariant manifolds and continuity of attractors.References
E.A.M. Abreu and A.N. Carvalho, Lower semicontinuity of attractors for parabolic problems with Dirichlet boundary conditons in varying domains, Matemática Contemporânea 27 (2004), 37–51.
J.M. Arrieta, F.D.M. Bezerra and A. N. Carvalho, Rate of convergence of Attractors for some singular perturbed parabolic problems, Topol. Methods Nonlinear Anal. 41 (2013), 229–253.
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, J.A. Langa and J.C. Robinson, Attractors for Infinite-Dimensional Non-Autonomous Dynamical Systems, Springer, London, 2010.
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.
E.N. Dancer and D. Daners, Domain perturbation of elliptic equations subject to Robin boundary conditions, J. Differential Equations 74 (1997), 86–132.
D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, Springer–Verlag, New York, 1980.
D. Henry, Perturbation of the Boundary in Partial Differential Equations, Cambridge University Press, Cambridge, 1996.
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Copyright (c) 2021 Leonardo Pires, Rodrigo A. Samprogna
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