### Abstract

This article is concerned with a dynamic blocking problem, originally motivated by the control of wild fires. It is assumed that the region R(t) ⊂ ℝ ^{2} burned by the fire is initially a disc, and expands with unit speed in all directions. To block the fire, a barrier Γ can be constructed in real time, so that the portion of the barrier constructed within time t has length ≤ σt, for some constant σ > 2. We prove that, among all barriers consisting of a single closed curve, the one which minimizes the total burned area is axisymmetric, and consists of an arc of circumference and two arcs of logarithmic spirals.

Original language | English (US) |
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Pages (from-to) | 125-145 |

Number of pages | 21 |

Journal | Calculus of Variations and Partial Differential Equations |

Volume | 45 |

Issue number | 1-2 |

DOIs | |

State | Published - Sep 1 2012 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

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## Cite this

Bressan, A., & Wang, T. (2012). On the optimal strategy for an isotropic blocking problem.

*Calculus of Variations and Partial Differential Equations*,*45*(1-2), 125-145. https://doi.org/10.1007/s00526-011-0453-4