本项目拟开展关于线性抛物方程脉冲时间最优控制问题的研究。脉冲控制是日常生活和实际应用中常用到的一种控制形式。本项目主要是希望得到相应时间最优控制的bang-bang性；然后，利用最优控制的bang-bang性对最优时间与最优控制进行更深入的研究。前者可能通过最大值原理与唯一延拓性得到。Bang-bang性是时间最优控制的一个重要性质，对它的研究不仅有理论意义而且也有应用背景。

In this project, we will study impluse time optimal control problems for linear parabolic equations. Impulse control is a kind of frequently used controls in daily life and practical applications. The main purpose of this project is to establish the bang-bang property for time optimal controls, and then, to make a further deep study on optimal time and optimal control through utilizing bang-bang property of time optimal controls. The bang-bang property may be obtained by combing maximum principle and unique continuation. The bang-bang property is an important property of time optimal controls. Studies on this property is significant from perspective of mathematical theory and applications.