1998
DOI: 10.1080/03605309808821394
|View full text |Cite
|
Sign up to set email alerts
|

Abstract: The relationship between random attractors and global attractors for dynamical systems is studied. If a partial differential equation is perturbed by an −small random term and certain hypotheses are satisfied, the upper semicontinuity of the random attractors is obtained as goes to zero. The results are applied to the Navier-Stokes equations and a problem of reaction-diffusion type, both perturbed by an additive white noise.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

4
124
0
1

Year Published

2001
2001
2023
2023

Publication Types

Select...
8
1

Relationship

2
7

Authors

Journals

citations
Cited by 142 publications
(129 citation statements)
references
References 19 publications
4
124
0
1
Order By: Relevance
“…Some support for this picture, at least for small ¼ , is given by the upper semicontinuity result in Caraballo et al (1998). We proved there that, as ¼ !…”
Section: Resultsmentioning
confidence: 82%
“…Some support for this picture, at least for small ¼ , is given by the upper semicontinuity result in Caraballo et al (1998). We proved there that, as ¼ !…”
Section: Resultsmentioning
confidence: 82%
“…However it may not be unique in general (see [10]). For example, consider the following nonautonomous ODE 19) which generates a process by setting ϕ(t, t 0 , x 0 ) = x(t; t 0 , x 0 ), where x(·; t 0 , x 0 ) denotes the unique solution to equation (3.19) satisfying x(t 0 ; t 0 , x 0 ) = x 0 .…”
Section: Nonautonomous Attractors For Processesmentioning
confidence: 99%
“…First, note that upper semicontinuity is a direct consequence of the continuity of the nonlinear processes {T η (t, τ ) | t ≥ τ } and the compactness of t∈R η∈[0,η 0 ] A η (t); for the standard argument, see the books by Hale [18], Robinson [27] and Temam [30] or the paper of Caraballo et al [6]. Here we prove that the attractor is also lower semicontinuous.…”
Section: Lower Semicontinuity Of Global Attractorsmentioning
confidence: 99%
“…Establishing the upper semicontinuity of attractors for autonomous dynamical systems is a relatively simple matter which depends only on obtaining uniform bounds on the attractors and proving continuity of the nonlinear semigroups (see the paper by Hale et al [17] and the books by Hale [18], Robinson [27] or Temam [30] for the autonomous case; for results derived in a non-autonomous framework, see Caraballo et al [6,7]). On Lower semicontinuity of attractors 1775 the other hand, results on the lower semicontinuity of attractors are much more difficult.…”
Section: Lower Semicontinuity Of Global Attractorsmentioning
confidence: 99%