Continuity of attractors for C^1 perturbations of a smooth domain
| dc.contributor.author | Barbosa, Pricila S. | |
| dc.contributor.author | Pereira, Antonio L. | |
| dc.date.accessioned | 2021-10-04T19:39:17Z | |
| dc.date.available | 2021-10-04T19:39:17Z | |
| dc.date.issued | 2020-09-21 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 31 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14604 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Parabolic problem | |
| dc.subject | Perturbation of the domain | |
| dc.subject | Global attractor | |
| dc.subject | Continuity of attractors | |
| dc.title | Continuity of attractors for C^1 perturbations of a smooth domain | |
| dc.type | Article |