关于边界控制的一维热方程达到可达状态的代价
On the cost of reaching an attainable state for the boundary-controlled 1-D heat equation
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中文总结 AI 辅助
研究一维热方程在Dirichlet边界控制下达到可达状态的代价，给出最小控制大小的估计，并在时间趋于零时最优。
中文摘要 AI 辅助
我们考虑实直线区间上的热方程，具有零初始条件和Dirichlet边界控制。我们研究在某个时间$T>0$达到可达状态的代价。具体而言，给定区间内一个已知可通过适当的边界控制达到的状态，我们根据该状态的适当范数来估计达到该状态的最小控制的大小。当时间范围趋于$0$时，我们的估计在某种意义下是最优的。
英文摘要
We consider the heat equation in an interval of the real line, with null initial condition, and Dirichlet boundary controls. We study the cost of reaching an attainable state at some time $T>0$. Precisely, given a state in the interval that we know is reachable by suitable boundary controls, we estimate the size of the smallest controls that reach it, in terms of an appropriate norm of this state. Our estimate is optimal in some sense as the time horizon goes to $0$.
