Mahmoud Baroun | Searcharxiv

arXiv2024

Insensitizing controls for stochastic parabolic equations with dynamic boundary conditions

In this paper, we continue the study of some controllability issues for the forward stochastic heat equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra forces in the noise parts. Under a strong measurability condition, and using a spectral inequality, we first establish an appropriate observability inequality for the corresponding adjoint system. Then, by the classical duality approach, the null and approximate controllability results are established.

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arXiv2024

Null Controllability for Backward Stochastic Parabolic Convection-Diffusion Equations with Dynamic Boundary Conditions

This paper is concerned with the null controllability for linear backward stochastic parabolic equations with dynamic boundary conditions and convection terms. Using the classical duality argument, the null controllability is obtained via an appropriate observability inequality of the corresponding adjoint forward stochastic parabolic equation. To prove this observability inequality, we develop a new global Carleman estimate for forward stochastic parabolic equations that contains some first-order terms in the weak divergence form. Our Carleman estimate is established by applying the duality technique. Moreover, an estimate of the null-control cost is provided.

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