论文标题
Carleman估计和可控性的随机退化抛物线热方程
Carleman Estimates and Controllability of Stochastic degenerate parabolic Heat Equations
论文作者
论文摘要
本文涉及一类随机退化抛物线方程的无效可控性。我们首先建立了具有乘法噪声的线性正向随机变性方程的全局卡尔曼估计。使用此估计，我们证明了向后方程的无效可控性，并获得了向前方程的可控性的部分结果。同样，使用新的卡尔曼估计值对向后方程进行加权函数，该方程在时间t = 0和双重方法嗡嗡声中不会消失，我们在两个控件的作用下获得了正随机变性方程的无效可控性。
This paper concerns the null controllability for a class of stochastic degenerate parabolic equations. We first establish a global Carleman estimate for a linear forward stochastic degenerate equation with multiplicative noise. Using this estimate we prove the null controllability of the backward equation and obtain a partial result for the controllability of the forward equation. Also, using a new Carleman estimate for backward equation with weighted function which does not vanish at time t = 0 and the duality method HUM we get the null controllability of a forward stochastic degenerate equation under the action of two controls.
