Controllability for semi-discrete semilinear stochastic parabolic operators
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910107299741696 |
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| author | Lecaros, Rodrigo Pérez, Ariel A. Prado, Manuel F. |
| author_facet | Lecaros, Rodrigo Pérez, Ariel A. Prado, Manuel F. |
| contents | In \cite{LPP:2025}, it was shown that, in arbitrary dimension, the spatial semi-discretization of a controlled stochastic parabolic operator is generically not null-controllable. Nevertheless, $ϕ$-null controllability results remain attainable. The present paper extends those results to semi-discrete semilinear stochastic operators in arbitrary dimension, whose nonlinearities may also depend on the first-order spatial derivatives. The approach relies on establishing a new Carleman estimate for the adjoint backward stochastic parabolic operator, which yields $ϕ$-null controllability for the associated linear system via a duality argument. The semilinear case is handeld by means of a fixed-point argument. As particular cases, our results recover the one-dimensional linear results of \cite{zhao:2024}, the multidimensional linear results of \cite{LPP:2025}, and the semilinear one-dimensional framework of \cite{WZ:2025} in the absence of gradient dependence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05155 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Controllability for semi-discrete semilinear stochastic parabolic operators Lecaros, Rodrigo Pérez, Ariel A. Prado, Manuel F. Optimization and Control In \cite{LPP:2025}, it was shown that, in arbitrary dimension, the spatial semi-discretization of a controlled stochastic parabolic operator is generically not null-controllable. Nevertheless, $ϕ$-null controllability results remain attainable. The present paper extends those results to semi-discrete semilinear stochastic operators in arbitrary dimension, whose nonlinearities may also depend on the first-order spatial derivatives. The approach relies on establishing a new Carleman estimate for the adjoint backward stochastic parabolic operator, which yields $ϕ$-null controllability for the associated linear system via a duality argument. The semilinear case is handeld by means of a fixed-point argument. As particular cases, our results recover the one-dimensional linear results of \cite{zhao:2024}, the multidimensional linear results of \cite{LPP:2025}, and the semilinear one-dimensional framework of \cite{WZ:2025} in the absence of gradient dependence. |
| title | Controllability for semi-discrete semilinear stochastic parabolic operators |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.05155 |