Exponential mixing for random nonlinear wave equations: weak dissipation and localized control
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911963699740672 |
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| author | Liu, Ziyu Wei, Dongyi Xiang, Shengquan Zhang, Zhifei Zhao, Jia-Cheng |
| author_facet | Liu, Ziyu Wei, Dongyi Xiang, Shengquan Zhang, Zhifei Zhao, Jia-Cheng |
| contents | We establish a new criterion for exponential mixing of random dynamical systems. Our criterion is applicable to a wide range of systems, including in particular dispersive equations. Its verification is in nature related to several topics, i.e., asymptotic compactness in dynamical systems, global stability of evolution equations, and localized control problems.
As an initial application, we exploit the exponential mixing of random nonlinear wave equations with degenerate damping, critical nonlinearity, and physically localized noise. The essential challenge lies in the fact that the weak dissipation and randomness interact in the evolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15058 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exponential mixing for random nonlinear wave equations: weak dissipation and localized control Liu, Ziyu Wei, Dongyi Xiang, Shengquan Zhang, Zhifei Zhao, Jia-Cheng Analysis of PDEs Dynamical Systems Optimization and Control Probability We establish a new criterion for exponential mixing of random dynamical systems. Our criterion is applicable to a wide range of systems, including in particular dispersive equations. Its verification is in nature related to several topics, i.e., asymptotic compactness in dynamical systems, global stability of evolution equations, and localized control problems. As an initial application, we exploit the exponential mixing of random nonlinear wave equations with degenerate damping, critical nonlinearity, and physically localized noise. The essential challenge lies in the fact that the weak dissipation and randomness interact in the evolution. |
| title | Exponential mixing for random nonlinear wave equations: weak dissipation and localized control |
| topic | Analysis of PDEs Dynamical Systems Optimization and Control Probability |
| url | https://arxiv.org/abs/2407.15058 |