Differential inclusions and the control of forest fires

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Abstract

This paper introduces a new class of variational problems for differential inclusions, motivated by the control of forest fires. The area burned by the fire at time t > 0 is modelled as the reachable set for a differential inclusion over(x, ̇) ∈ F (x), starting from an initial set R0. To block the fire, a wall can be constructed progressively in time, at a given speed. In this paper, we study the possibility of constructing a wall which completely encircles the fire. Moreover, we derive necessary conditions for an optimal strategy, which minimizes the total area burned by the fire.

Original languageEnglish (US)
Pages (from-to)179-207
Number of pages29
JournalJournal of Differential Equations
Volume243
Issue number2
DOIs
StatePublished - Dec 15 2007

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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