本项目拟展开关于带平方反比奇异位势的热方程的定量唯一延拓性估计式研究，以及它在偏微分方程控制理论中的应用。我们的首要目标是希望建立该类奇异方程解的定量唯一延拓性估计式，探究它的解在奇异点附近的小量传播性质；其次，希望通过上述定量唯一延拓性估计式导出它的解在正可测集上的能观性不等式，从而得到该类方程的时间最优控制问题的bang-bang性。

In this project, we will study the quantitative unique continuation estimate for some singular parabolic equations, and its applications in control theory. The main purpose is to build up the interpolation estimate of the strong unique continuation for this kind of singular parabolic equations, and consider the small propogation of the solution near the singularity point. Then, we will make use of the above quantitative estimate to derive the observability inequality from measurable sets of positive measure, from which we hope to obtain the bang-bang property for the time optimal control problem.