BLOCKING STRATEGIES FOR A FIRE CONTROL PROBLEM

Abstract

In this paper, we analyze different strategies, in a problem of optimal confinement of a forest fire. The area burned by the fire at time t > 0 is modeled as the reachable set for a differential inclusion ẋ ∈ F(x), starting from an initial set R 0 . To encircle the fire, a wall can be constructed progressively in time, at a given speed. We examine the minimum construction speed which is needed to completely encircle the fire, by means of one single wall. Different strategies are then compared, by a theoretical analysis and by numerical experiments, to determine which one minimizes the total burned area. We consider first the isotropic case, where the fire propagates uniformly in all directions, and then a more general case, where the wind blows the fire in one preferred direction.