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Invariant sample measures and random Liouville type theorem for a nonautonomous stochastic $ p $-Laplacian equation

  • *Corresponding author: Jintao Wang

    *Corresponding author: Jintao Wang 

Jintao Wang is supported by NSF of China (No. 11801190) and Xiaoqian Zhang is supported by Graduate Innovation Fund (No. 316202101029) of Wenzhou University in 2021

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  • We introduce invariant sample measures to nonautonomous random dynamical systems, and consider the dynamical behaviors of a nonautonomous stochastic $ p $-Laplacian equation with multiplicative noise on a bounded domain. We first use the asymptotic a priori estimate method to prove the existence of $ (L^2, L^q) $-pullback random attractors for the generated nonautonomous random dynamical system. Then, we establish the existence of invariant sample measures and random Liouville type theorem in $ L^2 $ for this equation. Moreover, the invariant sample measures are carried by $ W_0^{1, p}\cap L^q $.

    Mathematics Subject Classification: Primary: 35R60, 76F20; Secondary: 35B41.


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