论文标题
精制随机板方程的确切可控性
Exact Controllability for a Refined Stochastic Plate Equation
论文作者
论文摘要
广泛使用的随机板方程是经典板方程，该方程是由ITô积分术语扰动的。但是，众所周知，即使控件在漂移和扩散项以及边界上的任何地方都有效，该方程也不是完全可控的。从某种意义上说，这意味着在此模型中忽略了一些关键功能。然后，提出了一维精制的随机板方程，并在[28]中确定其确切的可控性。在本文中，通过新的全球卡尔曼估计，我们建立了具有两个内部控件和两个边界控制的多维精制随机板方程的确切可控性。此外，我们给出了缺乏确切可控性的结果，这表明两个内部控件的作用和至少一个边界控制是必要的。
A widely used stochastic plate equation is the classical plate equation perturbed by a term of Itô's integral. However, it is known that this equation is not exactly controllable even if the controls are effective everywhere in both the drift and the diffusion terms and also on the boundary. In some sense, this means that some key feature has been ignored in this model. Then, a one-dimensional refined stochastic plate equation is proposed and its exact controllability is established in [28]. In this paper, by means of a new global Carleman estimate, we establish the exact controllability of the multidimensional refined stochastic plate equation with two interior controls and two boundary controls. Moreover, we give a result about the lack of exact controllability, which shows that the action of two interior controls and at least one boundary control is necessary.
