On the optimal strategy for an isotropic blocking problem

Alberto Bressan, Tao Wang

Research output: Contribution to journalArticle

5 Scopus citations

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 languageEnglish (US)
Pages (from-to)125-145
Number of pages21
JournalCalculus of Variations and Partial Differential Equations
Volume45
Issue number1-2
DOIs
StatePublished - Sep 1 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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