Pires, Leonardo; Samprogna, Rodrigo A. Rate of convergence of global attractors for some perturbed reaction-diffusion equations under smooth perturbations of the domain. (English) Zbl 1483.35043 Topol. Methods Nonlinear Anal. 58, No. 2, 441-452 (2021). Summary: 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. Cited in 4 Documents MSC: 35B41 Attractors 35B20 Perturbations in context of PDEs 35K20 Initial-boundary value problems for second-order parabolic equations 35K57 Reaction-diffusion equations 35K58 Semilinear parabolic equations Keywords:domain perturbation; rate of attraction; reaction diffusion equations × Cite Format Result Cite Review PDF Full Text: DOI References: [1] E.A.M. Abreu and A.N. Carvalho, Lower semicontinuity of attractors for parabolic problems with Dirichlet boundary conditons in varying domains, Matematica Contemporanea 27 (2004), 37-51. · Zbl 1082.35037 [2] 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. · Zbl 1331.35053 [3] 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. · Zbl 1058.35028 [4] J.M. Arrieta, A.N. Carvalho and A. Rodriguez-Bernal, Attractors for parabolic problems with nonlinear boundary bondition. Uniform bounds, Comm. Partial Differential Equations 25 (2000), 1-37. · Zbl 0953.35021 [5] A.N. Carvalho, J.A. Langa and J.C. Robinson, Attractors for Infinite-Dimensional Non-Autonomous Dynamical Systems, Springer, London, 2010. · Zbl 1263.37002 [6] A.N. Carvalho and L. Pires, Rate of convergence of attractors for singularly perturbed semilinear problems, J. Math. Anal. Appl. 452 (2017), 258-296. · Zbl 1372.35046 [7] 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. · Zbl 1419.35121 [8] E.N. Dancer and D. Daners, Domain perturbation of elliptic equations subject to Robin boundary conditions, J. Differential Equations 74 (1997), 86-132. · Zbl 0886.35063 [9] D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, Springer-Verlag, New York, 1980. [10] D. Henry, Perturbation of the Boundary in Partial Differential Equations, Cambridge University Press, Cambridge, 1996. · Zbl 0857.65126 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.