dc.creator | Langa Rosado, José Antonio | es |
dc.creator | Cui, Hongyong | es |
dc.creator | Cunha, Arthur Cavalcante | es |
dc.date.accessioned | 2022-06-30T09:49:39Z | |
dc.date.available | 2022-06-30T09:49:39Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | Langa Rosado, J.A., Cui, H. y Cunha, A.C. (2021). Finite-Dimensionality of Tempered Random Uniform Attractors. Journal of Nonlinear Science, 32, 1-55. | |
dc.identifier.issn | 09388974 | es |
dc.identifier.issn | 14321467 | es |
dc.identifier.uri | https://hdl.handle.net/11441/134835 | |
dc.description.abstract | Finite-dimensional attractors play an important role in finite-dimensional reduction of
PDEs in mathematical modelization and numerical simulations. For non-autonomous
random dynamical systems, Cui and Langa (J Differ Equ, 263:1225–1268, 2017)
developed a random uniform attractor as a minimal compact random set which provides
a certain description of the forward dynamics of the underlying system by forward
attraction in probability. In this paper, we study the conditions that ensure a random
uniform attractor to have finite fractal dimension. Two main criteria are given, one
by a smoothing property and the other by a squeezing property of the system, and
neither of the two implies the other. The upper bound of the fractal dimension consists
of two parts: the fractal dimension of the symbol space plus a number arising from
the smoothing/squeezing property. As an illustrative application, the random uniform
attractor of a stochastic reaction–diffusion equation with scalar additive noise is stud ied, for which the finite-dimensionality in L2 is established by the squeezing approach
and that in H1
0 by the smoothing framework. In addition, a random absorbing set that
absorbs itself after a deterministic period of time is also constructed. | es |
dc.format | application/pdf | es |
dc.format.extent | 55 p. | es |
dc.language.iso | eng | es |
dc.publisher | Springer New York | es |
dc.relation.ispartof | Journal of Nonlinear Science, 32, 1-55. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Random uniform attractor | es |
dc.subject | Fractal dimension | es |
dc.subject | Finite-dimensionality | es |
dc.subject | Reaction–diffusion equation | es |
dc.title | Finite-Dimensionality of Tempered Random Uniform Attractors | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/publishedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales Y Análisis Numérico | es |
dc.relation.publisherversion | https://doi.org/10.1007/s00332-021-09764-8 | es |
dc.identifier.doi | 10.1007/s00332-021-09764-8 | es |
dc.journaltitle | Journal of Nonlinear Science | es |
dc.publication.volumen | 32 | es |
dc.publication.initialPage | 1 | es |
dc.publication.endPage | 55 | es |