Null controllability for stochastic fourth order semi-discrete parabolic equations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909190924009472 |
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| author | Wang, Yu Zhao, Qingmei |
| author_facet | Wang, Yu Zhao, Qingmei |
| contents | This paper is devoted to studying null controllability for a class of stochastic fourth order semi-discrete parabolic equations, where the spatial variable is discretized with finite difference scheme and the time is kept as a continuous variable. For this purpose, we establish a new global Carleman estimate for a backward stochastic fourth order semi-discrete parabolic operators, in which the large parameter is connected to the mesh size. A relaxed observability estimate is established for backward stochastic fourth order semi-discrete parabolic equations by this new Carleman estimate, with an explicit observability constant that depends on the discretization parameter and coefficients of lower order terms. Then, the $ϕ$-null controllability of the stochastic fourth order semi-discrete parabolic equations is proved using the standard duality technique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03257 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Null controllability for stochastic fourth order semi-discrete parabolic equations Wang, Yu Zhao, Qingmei Optimization and Control Probability This paper is devoted to studying null controllability for a class of stochastic fourth order semi-discrete parabolic equations, where the spatial variable is discretized with finite difference scheme and the time is kept as a continuous variable. For this purpose, we establish a new global Carleman estimate for a backward stochastic fourth order semi-discrete parabolic operators, in which the large parameter is connected to the mesh size. A relaxed observability estimate is established for backward stochastic fourth order semi-discrete parabolic equations by this new Carleman estimate, with an explicit observability constant that depends on the discretization parameter and coefficients of lower order terms. Then, the $ϕ$-null controllability of the stochastic fourth order semi-discrete parabolic equations is proved using the standard duality technique. |
| title | Null controllability for stochastic fourth order semi-discrete parabolic equations |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2405.03257 |