Upper semicontinuity of random attractors for non-compact random dynamical systems.
By Bixiang Wang. 2009
81 citations recorded by the source corpus.
The upper semicontinuity of random attractors for non-compact random dynamical systems is proved when the union of all perturbed random attractors is precompact with probability one. This result is applied to the stochastic Reaction-Diusion with white noise defined on the entire space R n .
Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/bd0ecf71162cbbb0439bcd188d0910a764b0f2ee
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In Computational Theory and Mathematics
In Computer Networks and Communications
In Control and Systems Engineering
Citations in the corpus
- Attractors of non-autonomous stochastic lattice systems in weighted spaces (2014, background): “Similar results can be found in [36, 37, 50] for deterministic equations and in [11, 56] for autonomous stochastic equations.”
- Asymptotic Behavior of Stochastic Wave Equations with Critical Exponents on R^3 (2008, background): “Recently, the existence and upper semicontinuity of random attractors for some equations on unbounded domains have been established in [7, 36, 37, 38] and [39], respectively.”
- Asymptotic behavior of stochastic wave equations with critical exponents on $\mathbb{R}^{3}$ (2008, background): “Recently, the existence and upper semicontinuity of random attractors for some equations on unbounded domains have been established in [7, 36, 37, 38] and [39], respectively.”
- Existence and continuity of bi-spatial random attractors and application to stochastic semilinear Laplacian equations (2015, background): “For instance, the authors in [11,29,32,33] have assumed pre-compactness of a union of attractors, while the authors in [9,10,22,26] have assumed the following condition: the family of attractors approaches to a compact set.”
- Existence and Upper Semicontinuity of Attractors for Stochastic Equations with Deterministic Non-autonomous Terms (2012, methodology): “We will overcome this difficulty by using uniform estimates on the tails of functions in random attractors as in [37].”