Artículo
Finite-Dimensionality of Tempered Random Uniform Attractors
Autor/es | Langa Rosado, José Antonio
![]() ![]() ![]() ![]() ![]() ![]() ![]() Cui, Hongyong Cunha, Arthur Cavalcante |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales Y Análisis Numérico |
Fecha de publicación | 2021 |
Fecha de depósito | 2022-06-30 |
Publicado en |
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Resumen | 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 ... 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. |
Cita | 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. |
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