TY - JOUR
T1 - Differential inclusions and the control of forest fires
AU - Bressan, Alberto
N1 - Funding Information:
This material is based upon work supported by the National Science Foundation under Grant No. 0505430.
PY - 2007/12/15
Y1 - 2007/12/15
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jde.2007.03.009
DO - 10.1016/j.jde.2007.03.009
M3 - Article
AN - SCOPUS:36048961455
SN - 0022-0396
VL - 243
SP - 179
EP - 207
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -