Three types of weak pullback attractors for lattice pseudo-parabolic equations driven by locally Lipschitz noise

Lianbing She; Nan Liu; Xin Li; Renhai Wang; Lianbing She; Nan Liu; Xin Li; Renhai Wang

doi:10.3934/era.2021028

Electronic Research Archive

2021, Volume 29, Issue 5: 3097-3119. doi: 10.3934/era.2021028

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Three types of weak pullback attractors for lattice pseudo-parabolic equations driven by locally Lipschitz noise

Lianbing She ^{1
,},
Nan Liu ^{2
,},
Xin Li ^{3
,},
Renhai Wang ^{2
,}

1.
School of Mathematics and Compute Science, Liupanshui Normal University, Liupanshui, Guizhou 553004, China
2.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
3.
College of Sciences, Beijing Information Science and Technology University, Beijing 100192, China

Received: 01 November 2020 Revised: 01 March 2021 Published: 15 April 2021
Primary: 37L55; Secondary: 37B55, 35B41, 35B40

The global well-posedness and long-time mean random dynamics are studied for a high-dimensional non-autonomous stochastic nonlinear lattice pseudo-parabolic equation with locally Lipschitz drift and diffusion terms. The existence and uniqueness of three different types of weak pullback mean random attractors as well as their relations are established for the mean random dynamical systems generated by the solution operators. This is the first paper to study the well-posedness and dynamics of the stochastic lattice pseudo-parabolic equation even when the nonlinear noise reduces to the linear one.
- Lattice pseudo-parabolic equation,
- locally Lipschitz noise,
- mean random dynamical systems,
- three types of weak attractors
Citation: Lianbing She, Nan Liu, Xin Li, Renhai Wang. Three types of weak pullback attractors for lattice pseudo-parabolic equations driven by locally Lipschitz noise[J]. Electronic Research Archive, 2021, 29(5): 3097-3119. doi: 10.3934/era.2021028

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Abstract

The global well-posedness and long-time mean random dynamics are studied for a high-dimensional non-autonomous stochastic nonlinear lattice pseudo-parabolic equation with locally Lipschitz drift and diffusion terms. The existence and uniqueness of three different types of weak pullback mean random attractors as well as their relations are established for the mean random dynamical systems generated by the solution operators. This is the first paper to study the well-posedness and dynamics of the stochastic lattice pseudo-parabolic equation even when the nonlinear noise reduces to the linear one.

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