Random Attractors for the Stochastic FitzHugh-Nagumo System on Unbounded Domains

By Bixiang Wang. 2008

70 citations recorded by the source corpus.

The existence of a random attractor for the stochastic FitzHugh-Nagumo system defined on an unbounded domain is established. The pullback asymptotic compactness of the stochastic system is proved by uniform estimates on solutions for large space and time variables. These estimates are obtained by a cut-off technique.

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

View Paper: https://www.semanticscholar.org/paper/901e68269ebc973a561e7ae5ae89a015ba7aee51

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In Computational Theory and Mathematics

In Computer Networks and Communications

In Control and Systems Engineering

Citations in the corpus

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.”
Upper semicontinuity of random attractors for non-compact random dynamical systems. (2009, background): “Nevertheless, the existence of such attractors for some stochastic PDEs on unbounded domains has been proved in [4, 27, 28, 29, 30] recently.”
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.”
Sufficient and Necessary Criteria for Existence of Pullback Attractors for Non-compact Random Dynamical Systems (2012, background): “symptotic compactness does not require a system to have a compact pullback absorbing set, and hence it works for dissipative ODEs on inﬁnite 2 lattices as well as PDEs on unbounded domains, see e.g., [5, 6, 30, 31, 32]. In this paper, we will further extend the concept of asymptotic compactness to t”
Random attractors for a class of stochastic partial differential equations driven by general additive noise (2010, unknown): “46 41 v2 [ m at AMS Subject Classification: 35B41, 60H15, 37L30, 35B40 Keywords: Random attractor; Lévy noise; fractional Brownian motion; stochastic evolution equations; porous media equations; p-Laplace equation; reaction-diffusion equations.”