### 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) |
---|---|

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 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

*Calculus of Variations and Partial Differential Equations*,

*45*(1-2), 125-145. https://doi.org/10.1007/s00526-011-0453-4

}

*Calculus of Variations and Partial Differential Equations*, vol. 45, no. 1-2, pp. 125-145. https://doi.org/10.1007/s00526-011-0453-4

**On the optimal strategy for an isotropic blocking problem.** / Bressan, Alberto; Wang, Tao.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the optimal strategy for an isotropic blocking problem

AU - Bressan, Alberto

AU - Wang, Tao

PY - 2012/9/1

Y1 - 2012/9/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84865651022&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865651022&partnerID=8YFLogxK

U2 - 10.1007/s00526-011-0453-4

DO - 10.1007/s00526-011-0453-4

M3 - Article

VL - 45

SP - 125

EP - 145

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

SN - 0944-2669

IS - 1-2

ER -