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arXiv · 2604.05155

Controllability for semi-discrete semilinear stochastic parabolic operators

Rodrigo Lecaros·Ariel A. Pérez·Manuel F. Prado
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Abstract

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, $\phi$-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 $\phi$-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.

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Rodrigo Lecaros, Ariel A. Pérez, Manuel F. Prado. 2026-04-06. Controllability for semi-discrete semilinear stochastic parabolic operators. https://arxiv.org/abs/2604.05155

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