Carleman Estimates of Refined Stochastic Beam Equations and Applications (Ji-Feng Zhang)

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05 29, 2023

  This paper is devoted to establishing global Carleman estimates for refined stochastic beam equations. First, by establishing a fundamental weighted identity, two Carleman estimates are derived with different weight functions for the refined stochastic beam equation, which is a coupled system consisting of a stochastic ordinary differential equation and a stochastic partial differential equation. As applications of these Carleman estimates, the exact controllability of the refined system is proved by the least controls in some sense. Different from classical stochastic beam equations, the refined one is exactly controllable at any time. Meanwhile, the uniqueness of an inverse source problem for refined stochastic beam equations is obtained without any requirement on the initial and terminal data.

  

  Publication:

  SIAM Journal on Control and Optimization, Vol. 60, Iss. 5(2022), 10.1137/21M1463513

   

  Author:

  Yongyi Yu

  Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

  Ji-Feng Zhang

  Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

  School of Mathematics Sciences, University of Chinese Academy of Sciences, Beijing 100149, China

  Email: jif@iss.ac.cn

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