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arXiv · 2503.03596

Carleman estimate for semi-discrete stochastic parabolic operators in arbitrary dimension and applications to controllability

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

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 $\phi$-null controllability by duality arguments.

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Rodrigo Lecaros, Ariel A. Pérez, Manuel F. Prado. 2025-03-05. Carleman estimate for semi-discrete stochastic parabolic operators in arbitrary dimension and applications to controllability. https://arxiv.org/abs/2503.03596

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