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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Finite-Dimensionality of Tempered Random Uniform Attractors

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Author(s):
Cui, Hongyong [1] ; Cunha, Arthur C. [2] ; Langa, Jose A. [3]
Total Authors: 3
Affiliation:
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074 - Peoples R China
[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Campus Sao Carlos, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
[3] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, Apdo Cotreos 1160, Seville 41080 - Spain
Total Affiliations: 3
Document type: Journal article
Source: JOURNAL OF NONLINEAR SCIENCE; v. 32, n. 1 FEB 2022.
Web of Science Citations: 0
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 studied, for which the finite-dimensionality in L-2 is established by the squeezing approach and that in H-0(1) by the smoothing framework. In addition, a random absorbing set that absorbs itself after a deterministic period of time is also constructed. (AU)

FAPESP's process: 16/26289-5 - Estimates of the Fractal Dimension of Attractors for Autonomous and Non-Autonomous Dynamical Systems
Grantee:Arthur Cavalcante Cunha
Support Opportunities: Scholarships in Brazil - Doctorate
FAPESP's process: 18/10634-0 - Estimates of the fractal dimension of attractors for autonomous and non-autonomous dynamical systems: applications
Grantee:Arthur Cavalcante Cunha
Support Opportunities: Scholarships abroad - Research Internship - Doctorate