报告题目：Dynamic blocking problems for a model of fire confinement
报告人：Alberto Bressan （Pennsylvania State University）
报告时间：2018年12月12日（星期三） 下午 15：30-16:30
摘要：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.
报告人介绍：Alberto Bressan，美国宾州州立大学Eberly Family讲席教授，主要从事双曲守恒律，拉格朗日系统的脉冲控制，非合作微分策略等问题的研究。2002年国际数学家大会一小时邀请报告，美国数学会会士，曾获得Bôcher Memorial Prize，A. Feltrinelli prize，Analysis of Partial Differential Equations Prize of the SIAM等多项荣誉。担任十几个国际重要期刊编委，包括Arch. Rational Mech. Anal., J. Differential Eqn., SIAM J. Math. Anal., Discrete Cont. Dyn.等。多次在国际会议上做邀请报告，发表近200篇学术论文及多本专著。