Pullback attractor in H1 for nonautonomous stochastic reaction-diffusion equations on ℝn

Linfang Liu; Xianlong Fu; Yuncheng You

doi:10.3934/dcdsb.2017143

Pullback attractor in H¹ for nonautonomous stochastic reaction-diffusion equations on ℝⁿ

Linfang Liu, Xianlong Fu, Yuncheng You

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper we study the asymptotic dynamics of the weak solutions of nonautonomous stochastic reaction-diffusion equations driven by a time-dependent forcing term and the multiplicative noise. By conducting the uniform estimates we show that the cocycle generated by this SRDE has a pull-back (L², H¹) absorbing set and it is pullback asymptotically compact through the pullback attening approach. The existence of a pullback (L², H¹) random attractor for this random dynamical system in space H¹(ℝⁿ) is proved.

Original language	English
Pages (from-to)	3629-3651
Number of pages	23
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	22
Issue number	10
DOIs	https://doi.org/10.3934/dcdsb.2017143
State	Published - Dec 2017

Keywords

Pullback asymptotic compactness
Pullback attening property
Pullback random attractor
Stochastic reaction-diffusion equation

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10.3934/dcdsb.2017143

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abstract = "In this paper we study the asymptotic dynamics of the weak solutions of nonautonomous stochastic reaction-diffusion equations driven by a time-dependent forcing term and the multiplicative noise. By conducting the uniform estimates we show that the cocycle generated by this SRDE has a pull-back (L2, H1) absorbing set and it is pullback asymptotically compact through the pullback attening approach. The existence of a pullback (L2, H1) random attractor for this random dynamical system in space H1(ℝn) is proved.",

keywords = "Pullback asymptotic compactness, Pullback attening property, Pullback random attractor, Stochastic reaction-diffusion equation",

author = "Linfang Liu and Xianlong Fu and Yuncheng You",

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N2 - In this paper we study the asymptotic dynamics of the weak solutions of nonautonomous stochastic reaction-diffusion equations driven by a time-dependent forcing term and the multiplicative noise. By conducting the uniform estimates we show that the cocycle generated by this SRDE has a pull-back (L2, H1) absorbing set and it is pullback asymptotically compact through the pullback attening approach. The existence of a pullback (L2, H1) random attractor for this random dynamical system in space H1(ℝn) is proved.

AB - In this paper we study the asymptotic dynamics of the weak solutions of nonautonomous stochastic reaction-diffusion equations driven by a time-dependent forcing term and the multiplicative noise. By conducting the uniform estimates we show that the cocycle generated by this SRDE has a pull-back (L2, H1) absorbing set and it is pullback asymptotically compact through the pullback attening approach. The existence of a pullback (L2, H1) random attractor for this random dynamical system in space H1(ℝn) is proved.

KW - Pullback asymptotic compactness

KW - Pullback attening property

KW - Pullback random attractor

KW - Stochastic reaction-diffusion equation

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JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 10

ER -

Pullback attractor in H¹ for nonautonomous stochastic reaction-diffusion equations on ℝⁿ

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Keywords

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