Continuity of attractors for C^1 perturbations of a smooth domain
Date
2020-09-21
Authors
Barbosa, Pricila S.
Pereira, Antonio L.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We 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.
Description
Keywords
Parabolic problem, Perturbation of the domain, Global attractor, Continuity of attractors
Citation
Barbosa, 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.
Rights
Attribution 4.0 International