Invariant sample measures and sample statistical solutions for nonautonomous stochastic lattice Cahn-Hilliard equation with nonlinear noise
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909178411352064 |
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| author | Wang, Jintao Zhu, Dongdong Li, Chunqiu |
| author_facet | Wang, Jintao Zhu, Dongdong Li, Chunqiu |
| contents | We consider a stochastic lattice Cahn-Hilliard equation with nonautonomous nonlinear noise. First, we prove the existence of pullback random attractors in $\ell^2$ for the generated nonautonomous random dynamical system. Then, we construct the time-dependent invariant sample Borel probability measures based on the pullback random attractor. Moreover, we develop a general stochastic Liouville type equation for nonautonomous random dynamical systems and show that the invariant sample measures obtained satisfy the stochastic Liouville type equation. At last, we define a new kind of statistical solution -- sample statistical solution corresponding to the invariant sample measures and show that each family of invariant sample measures is a sample statistical solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14798 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invariant sample measures and sample statistical solutions for nonautonomous stochastic lattice Cahn-Hilliard equation with nonlinear noise Wang, Jintao Zhu, Dongdong Li, Chunqiu Probability Dynamical Systems 60H10, 37L60, 37L30, 37L40 We consider a stochastic lattice Cahn-Hilliard equation with nonautonomous nonlinear noise. First, we prove the existence of pullback random attractors in $\ell^2$ for the generated nonautonomous random dynamical system. Then, we construct the time-dependent invariant sample Borel probability measures based on the pullback random attractor. Moreover, we develop a general stochastic Liouville type equation for nonautonomous random dynamical systems and show that the invariant sample measures obtained satisfy the stochastic Liouville type equation. At last, we define a new kind of statistical solution -- sample statistical solution corresponding to the invariant sample measures and show that each family of invariant sample measures is a sample statistical solution. |
| title | Invariant sample measures and sample statistical solutions for nonautonomous stochastic lattice Cahn-Hilliard equation with nonlinear noise |
| topic | Probability Dynamical Systems 60H10, 37L60, 37L30, 37L40 |
| url | https://arxiv.org/abs/2404.14798 |