|Title||Existence of optimal strategies for a fire confinement problem.|
|Publication Type||Journal Article|
|Year of Publication||2009|
|Authors||Bressan A., De Lellis C.|
|Journal||Communications on Pure and Applied Mathematics|
|Type of Article||other|
|Keywords||Applied Mathematics, General Mathematics|
We consider a class of variational problems for differential inclusions related to the control of forest fires. The area burned by the fire at time t \ensuremath> 0 is modeled as the reachable set for a differential inclusion F(x) starting from an initial set R0. To block the fire, a barrier can be constructed progressively in time at a given speed. In this paper we prove the existence of an optimal strategy, which minimizes the value of the area destroyed by the fire plus the cost of constructing the barrier.
Comm. Pure Appl. Math. 62 (2009), no. 6, 789–830.