Random Attractors for the Stochastic Benjamin-Bona-Mahony Equation on Unbounded Domains

By Bixiang Wang. 2008

162 citations recorded by the source corpus.

We prove the existence of a compact random attractor for the stochastic Benjamin-Bona-Mahony Equation defined on an unbounded domain. This random attractor is invariant and attracts every pulled-back tempered random set under the forward flow. The asymptotic compactness of the random dynamical system is established by a tail-estimates method, which shows that the solutions are uniformly asymptotically small when space and time variables approach infinity.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/19254d7704ed1048347dc0c093fbd4a2ae94a112

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Citations in the corpus

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 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.”
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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.”
Existence, Stability and Bifurcation of Random Complete and Periodic Solutions of Stochastic Parabolic Equations (2013, background): “ous stochastic one. The concept of random attractor for autonomous systems was introduced in [18, 25, 44], and the existence of such attractors have been established for various equations, see, e.g., [1, 4, 5, 6, 7, 8, 9, 10, 16, 17, 18, 19, 25, 26, 27, 32, 33, 44, 49, 50]. For the existence of inva”
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.”
Random attractors for stochastic reaction–diffusion equations on unbounded domains (2009, background): “Aswe know, the asymptotic behavior of a randomdynamical system (RDS) is characterized by random attractors, which were first introduced by Crauel and Flandoli [3] and Schmalfuss [4] and then developed in [1, 2, 5–12] and among others.”
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.”
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.”