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Dynamic blocking problems for a model of fire confinement


Academic Report

Title: Dynamic blocking problems for a model of fire confinement

Reporter: Alberto Bressan (Pennsylvania State University)

Time: December 12, 2018 (Wednesday) PM 15:30-16:30

Location: B1412# room, Innovation Park Building

Contact: YU Fang(tel:84708351-8025)


Abstract: A classical problem in the Calculus of Variations is to find a curve with given length L, 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 are motivated by the control of forest fires, where firemen seek to construct a barrier, minimizing the total area of the region burned by the fire. In this mathematical 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?
Results on the existence or non-existence of a blocking strategy will be presented, together with an example where the optimal barrier can be explicitly computed. I shall conclude the talk mentioning an open problem (easy to understand also for non-mathematicians), for which a $$ prize is still offered.


The brief introduction to the reporter: Alberto Bressan, Professor of Eberly Family, Pennsylvania State University, USA, is mainly engaged in the study of hyperbolic conservation laws, impulse control of Lagrangian systems, non-cooperative differential strategies and other issues. He made an hour's invitation report at the 2002 International Conference of Mathematicians. He was also a member of the American Mathematics Association. He had won many honors, such as Brhcher Memorial Prize, A. Feltrinelli Prize, Analysis of Partial Differential Equations Prize of the SIAM. He served as editor of more than a dozen international journals, including Arch. Rational Mech. Anal., J. Differential Eqn., SIAM J. Math. Anal., Discrete Cont. Dyn. He has made many Invitational reports at international conferences, published nearly 200 academic papers and many monographs.