A Stochastic Weakly Damped, Forced KdV-BO Equation

A Stochastic Weakly Damped, Forced KdV-BO Equation

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 s...

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Main Author: Guolian Wang
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/576087
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spelling doaj-acb9c72d43e64e9ca2447f1d7253875d2020-11-24T23:58:52ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/576087576087A Stochastic Weakly Damped, Forced KdV-BO EquationGuolian Wang0Department of Mathematics, Tongji University, Shanghai 200092, ChinaWe 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 H1(ℝ).http://dx.doi.org/10.1155/2014/576087
collection DOAJ
language English
format Article
sources DOAJ
author Guolian Wang
spellingShingle Guolian Wang
A Stochastic Weakly Damped, Forced KdV-BO Equation
Abstract and Applied Analysis
author_facet Guolian Wang
author_sort Guolian Wang
title A Stochastic Weakly Damped, Forced KdV-BO Equation
title_short A Stochastic Weakly Damped, Forced KdV-BO Equation
title_full A Stochastic Weakly Damped, Forced KdV-BO Equation
title_fullStr A Stochastic Weakly Damped, Forced KdV-BO Equation
title_full_unstemmed A Stochastic Weakly Damped, Forced KdV-BO Equation
title_sort stochastic weakly damped, forced kdv-bo equation
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description 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 H1(ℝ).
url http://dx.doi.org/10.1155/2014/576087
work_keys_str_mv AT guolianwang astochasticweaklydampedforcedkdvboequation
AT guolianwang stochasticweaklydampedforcedkdvboequation
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