Stability of random attractors for non-autonomous stochastic $ p $-Laplacian lattice equations with random viscosity

Xin Liu; Xin Liu

doi:10.3934/math.2025339

AIMS Mathematics

2025, Volume 10, Issue 3: 7396-7413. doi: 10.3934/math.2025339

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Research article

Stability of random attractors for non-autonomous stochastic $ p $-Laplacian lattice equations with random viscosity

Xin Liu ^,

School of Mathematics, Hohai University, Nanjing, Jiangsu 210098, China

Received: 19 December 2024 Revised: 17 March 2025 Accepted: 19 March 2025 Published: 31 March 2025
MSC : 35B40, 35B41, 37L55

In this paper, we investigate the stability of pullback random attractors for non-autonomous stochastic $ p $-Laplacian lattice systems, which are influenced by random viscosity and multiplicative white noise. Under appropriate conditions, we first prove the existence and uniqueness of these pullback random attractors and then establish their backward compactness. To ensure their measurability, we demonstrate the equivalence of two different classes of attractors across two distinct universes. Finally, we examine the asymptotic stability of these pullback random attractors by assuming that the time-dependent external forcing term converges to a time-independent external force as time approaches negative infinity.
- random attractors,
- stochastic $ p $-Laplacian lattice system,
- asymptotically autonomous stability,
- multiplicative white noise
Citation: Xin Liu. Stability of random attractors for non-autonomous stochastic $ p $-Laplacian lattice equations with random viscosity[J]. AIMS Mathematics, 2025, 10(3): 7396-7413. doi: 10.3934/math.2025339

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Abstract

In this paper, we investigate the stability of pullback random attractors for non-autonomous stochastic $ p $-Laplacian lattice systems, which are influenced by random viscosity and multiplicative white noise. Under appropriate conditions, we first prove the existence and uniqueness of these pullback random attractors and then establish their backward compactness. To ensure their measurability, we demonstrate the equivalence of two different classes of attractors across two distinct universes. Finally, we examine the asymptotic stability of these pullback random attractors by assuming that the time-dependent external forcing term converges to a time-independent external force as time approaches negative infinity.

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