Barbosa, Pricila S.Pereira, Antonio L.2021-10-042021-10-042020-09-21Barbosa, P. S., & Pereira, A. L. (2020). Continuity of attractors for C^1 perturbations of a smooth domain. <i>Electronic Journal of Differential Equations, 2020</i>(97), pp. 1-31.1072-6691https://hdl.handle.net/10877/14604We consider a family of semilinear parabolic problems with non-linear boundary conditions ut(x, t) = ∆u(x, t) - αu(x, t) + ƒ(u(x, t)), x ∈ Ωɛ, t > 0, ∂u/∂N (x, t) = g(u(x, t)), x ∈ ∂Ωɛ, t > 0, where Ω0 ⊂ ℝn is a smooth (at least C2) domain, Ωɛ = hɛ(Ω0) and hɛ is a family of diffeomorphisms converging to the identity in the C1-norm. Assuming suitable regularity and dissipative conditions for the nonlinearities, we show that the problem is well posed for ɛ > 0 sufficiently small in a suitable scale of fractional spaces, the associated semigroup has a global attractor Aɛ and the family {Aɛ} is continuous at ɛ = 0.Text31 pages1 file (.pdf)enAttribution 4.0 InternationalParabolic problemPerturbation of the domainGlobal attractorContinuity of attractorsArticle