论文标题
关于最佳动态阻塞策略的规律性
On the Regularity of Optimal Dynamic Blocking Strategies
论文作者
论文摘要
该论文研究了一个动态阻塞问题，这是由最佳火灾限制模型的动机。虽然大火可以在各个方向上以单位速度扩展，但障碍物是实时构建的。寻求最佳的策略，最大程度地减少燃烧区域的总价值以及建筑成本。众所周知，最佳障碍存在。通常，它们是紧凑，连接，可整流的集合的可计数结合。本文的主要结果表明，最佳屏障无处不在。证明依赖于可及的集合和火灾的最佳轨迹的新估计，从而在存在障碍物的情况下解决了最小的时间问题。
The paper studies a dynamic blocking problem, motivated by a model of optimal fire confinement. While the fire can expand with unit speed in all directions, barriers are constructed in real time. An optimal strategy is sought, minimizing the total value of the burned region, plus a construction cost. It is well known that optimal barriers exists. In general, they are a countable union of compact, connected, rectifiable sets. The main result of the present paper shows that optimal barriers are nowhere dense. The proof relies on new estimates on the reachable sets and on optimal trajectories for the fire, solving a minimum time problem in the presence of obstacles.
