Abstract
This article is concerned with a dynamic blocking problem, originally motivated by the control of wild fires. It is assumed that the region \({R(t) \subset \mathbb {R}^2}\) 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.
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Communicated by L. Ambrosio.
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Bressan, A., Wang, T. On the optimal strategy for an isotropic blocking problem. Calc. Var. 45, 125–145 (2012). https://doi.org/10.1007/s00526-011-0453-4
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DOI: https://doi.org/10.1007/s00526-011-0453-4