论文标题
随机半线性抛物线方程的全局无效控制性
Global null-controllability for stochastic semilinear parabolic equations
论文作者
论文摘要
在本文中，我们证明了前向（向后）半线性随机抛物线方程的小型全局无效控制性，在漂移和扩散项中具有全球Lipschitz非线性（在漂移项中）。特别是，我们解决了2009年S. Tang和X. Zhang提出的一个空旷的问题。我们对控制线性随机系统的经典策略提出了新的转折。通过采用新的精制Carleman估计，我们可以在具有源项的线性系统的加权空间中获得可控性结果。这里的主要新颖性是Carleman参数是显式的，然后在Banach固定点方法中使用。这使得在研究随机PDE的可控性问题时缺乏紧凑性嵌入的众所周知的问题。
In this paper, we prove the small-time global null-controllability of forward (resp. backward) semilinear stochastic parabolic equations with globally Lipschitz nonlinearities in the drift and diffusion terms (resp. in the drift term). In particular, we solve the open question posed by S. Tang and X. Zhang, in 2009. We propose a new twist on a classical strategy for controlling linear stochastic systems. By employing a new refined Carleman estimate, we obtain a controllability result in a weighted space for a linear system with source terms. The main novelty here is that the Carleman parameters are made explicit and are then used in a Banach fixed point method. This allows to circumvent the well-known problem of the lack of compactness embeddings for the solutions spaces arising in the study of controllability problems for stochastic PDEs.
