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dc.contributor.authorBarbosa, Pricila S. ( )
dc.contributor.authorPereira, Antonio L. ( )
dc.date.accessioned2021-10-04T19:39:17Z
dc.date.available2021-10-04T19:39:17Z
dc.date.issued2020-09-21
dc.identifier.citationBarbosa, P. S., & Pereira, A. L. (2020). Continuity of attractors for C^1 perturbations of a smooth domain. Electronic Journal of Differential Equations, 2020(97), pp. 1-31.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14604
dc.description.abstractWe 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.formatText
dc.format.extent31 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectParabolic problemen_US
dc.subjectPerturbation of the domainen_US
dc.subjectGlobal attractoren_US
dc.subjectContinuity of attractorsen_US
dc.titleContinuity of attractors for C^1 perturbations of a smooth domainen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
dc.description.departmentMathematics


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