Alberto Bressan
Pennsylvania State University
Dynamic blocking problems for a model of fire confinement
A classical problem in the Calculus of Variations asks to find a curve with a given length, which encloses a region of maximum area.
In this talk I shall discuss the seemingly opposite problem of finding curves enclosing a region with MINIMUM area. Problems of this kind arise naturally in the control of forest fires, when firemen seek to construct a barrier, minimizing the total area of the region burned by the fire. In this model, a key parameter is the speed at which the barrier is constructed. If the construction rate is too slow, the fire cannot be contained.
The talk will focus on two main questions:
Can the fire be confined to a bounded region?
If so, is there an optimal strategy for constructing the barrier, minimizing the total value of the land destroyed by the fire?
Based on the analysis of a corresponding Hamilton-Jacobi equation with obstacles, results on the existence or non-existence of a blocking strategy will be discussed, together with a new regularity result for optimal barriers, and an example where the optimal strategy can be explicitly described.
