数学与统计学院知识库

本文是作者在阅读的关于正向和倒向随机抛物方程的零可控性问题的文献基础上做的关于此问题的文献综述. 主要内容是通过全局 Carleman 估计对具有一般系数的线性正向和倒向随机抛物方程建立了可观测性估计, 进而建立关于随机抛物方程的 Carleman 不等式, 进一步证明了该类随机抛物方程解的零可控性. 最后介绍了这种零可控性目前的一些研究展望和应用.

This paper is a review of the work on the null controllability of forward and backward stochastic parabolic equations. The main content is to establish the observability estimates through the global Carleman estimates for linear backward and forward stochstic parabolic equations with general coefficients, which gives the Carleman inequalities for forward and backward stochastic parabolic equations. Finally, null controllability of stochastic forward and backward parabolic equations are derived respectively. Then, some applications and research prospect of this kind of null controllability currently are introduced as a supplement.