Convergence of bi-spatial pullback random attractors and stochastic Liouville type equations for nonautonomous stochastic p-Laplacian lattice system

2024/06/11 by Jintao Wang, Wang, Jintao, Qinghai Peng +3
Engineering · Computer Science · Mathematics · #Stability and Controllability of Differential Equations #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2406.07192

Abstract

We consider convergence properties of the long-term behaviors with respect to the coefficient of the stochastic term for a nonautonomous stochastic p-Laplacian lattice equation with multiplicative noise. First, the upper semi-continuity of pullback random (ℓ²,ℓ^q)-attractor is proved for each q∈[1,+∞). Then, a convergence result of the time-dependent invariant sample Borel probability measures is obtained in ℓ². Next, we show that the invariant sample measures satisfy a stochastic Liouville type equation and a termwise convergence of the stochastic Liouville type equations is verified. Furthermore, each family of the invariant sample measures is turned out to be a sample statistical solution, which hence also fulfills a convergence consequence.

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