A Stochastic Weakly Damped, Forced KdV-BO Equation

Guolian Wang

doi:10.1155/2014/576087

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Home > Journals > Abstr. Appl. Anal. > Volume 2014 > Issue SI66 > Article

2014 A Stochastic Weakly Damped, Forced KdV-BO Equation

Guolian Wang

Abstr. Appl. Anal. 2014(SI66): 1-8 (2014). DOI: 10.1155/2014/576087

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Abstract

We investigate the long time behavior of the damped, forced KdV-BO equation driven by white noise. We first show that the global solution generates a random dynamical system. By energy type estimates and dispersive properties, we then prove that this system possesses a weak random attractor in the space ${H}^{1}(\Bbb R)$ .