Null controllability for stochastic fourth order semi-discrete parabolic equations

Yu Wang; Qingmei Zhao

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arXiv · 2405.03257

Null controllability for stochastic fourth order semi-discrete parabolic equations

Yu Wang·Qingmei Zhao

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Abstract

This paper is devoted to studying null controllability for a class of stochastic fourth order semi-discrete parabolic equations, where the spatial variable is discretized with finite difference scheme and the time is kept as a continuous variable. For this purpose, we establish a new global Carleman estimate for a backward stochastic fourth order semi-discrete parabolic operators, in which the large parameter is connected to the mesh size. A relaxed observability estimate is established for backward stochastic fourth order semi-discrete parabolic equations by this new Carleman estimate, with an explicit observability constant that depends on the discretization parameter and coefficients of lower order terms. Then, the $\phi$-null controllability of the stochastic fourth order semi-discrete parabolic equations is proved using the standard duality technique.

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Yu Wang, Qingmei Zhao. 2024-05-06. Null controllability for stochastic fourth order semi-discrete parabolic equations. https://arxiv.org/abs/2405.03257

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