Carleman estimate for semi-discrete stochastic parabolic operators in arbitrary dimension and applications to controllability
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915419233714176 |
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| author | Lecaros, Rodrigo Pérez, Ariel A. Prado, Manuel F. |
| author_facet | Lecaros, Rodrigo Pérez, Ariel A. Prado, Manuel F. |
| contents | This paper considers a semi-discrete forward stochastic parabolic operator with homogeneous Dirichlet conditions in arbitrary dimensions. We show the lack of null controllability for a spatial semi-discretization of a null-controllable stochastic parabolic system from any initial datum. However, by proving a new Carleman estimate for its semi-discrete backward stochastic adjoint system, we achieve a relaxed observability inequality, which is applied to derivative $ϕ$-null controllability by duality arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03596 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Carleman estimate for semi-discrete stochastic parabolic operators in arbitrary dimension and applications to controllability Lecaros, Rodrigo Pérez, Ariel A. Prado, Manuel F. Optimization and Control This paper considers a semi-discrete forward stochastic parabolic operator with homogeneous Dirichlet conditions in arbitrary dimensions. We show the lack of null controllability for a spatial semi-discretization of a null-controllable stochastic parabolic system from any initial datum. However, by proving a new Carleman estimate for its semi-discrete backward stochastic adjoint system, we achieve a relaxed observability inequality, which is applied to derivative $ϕ$-null controllability by duality arguments. |
| title | Carleman estimate for semi-discrete stochastic parabolic operators in arbitrary dimension and applications to controllability |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.03596 |