Non--autonomous and random attractors for delay random semilinear equations without uniqueness

By Tomás Caraballo, María J. Garrido-Atienza, B. Schmalfuβ, José Valero. 2008

176 citations recorded by the source corpus.

We first prove the existence and uniqueness of pullback and random attractors for abstract multi-valued non-autonomous and random dynamical systems. The standard assumption of compactness of these systems can be replaced by the assumption of asymptotic compactness. Then, we apply the abstract theory to handle a random reaction-diffusion equation with memory or delay terms which can be considered on the complete past defined by $\mathbb{R}^{-}$. In particular, we do not assume the uniqueness of solutions of these equations.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/28b28924d7f5706bae61a86cbd6e7cd27bd8a2c4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Computer Networks and Communications

In Control and Systems Engineering

Citations in the corpus

Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains (2013, background): “Since then, such attractors for autonomous stochastic PDEs have been studied in [6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 31] in bounded domains, and in [4, 33, 34] in unbounded domains.”
Attractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearities (2012, methodology): “Now we recall two general results on the existence and uniqueness of pullback and random attractors associated to MNDS and MRDS respectively, which were proved in [11].”
Asymptotic behavior of random fitzhugh-nagumo systems driven by colored noise (2017, background): “The concept of random attractors was introduced in [18, 21, 44] and further studied in [6, 7, 8, 9, 11, 12, 13, 15, 16, 18, 22, 23, 24, 26, 32, 37, 40, 50, 51] for the autonomous stochastic equations; and in [2, 14, 19, 27, 28, 52, 53, 54] for the non-autonomous stochastic equations.”
Pullback attractors for 2D-Navier-Stokes equations with delays in continuous and sub-linear operators (2009, result): “Our results here are related to those in [3], although the presentation there is random instead of deterministic (which is our case); some of them, but for a universe without relating it with that of fixed bounded sets, are also exposed in [4].”