On the optimal strategy for an isotropic blocking problem |
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Authors: | Alberto Bressan Tao Wang |
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Affiliation: | 1. Department of Mathematics, Penn State University, University Park, PA, 16802, USA
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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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