Logo

Distinguished Lecture in Celebration of the 10th Anniversary of INS—— Dynamic Blocking Problems for a Model of Fire Confinement

6ea2c51dab5a6e0ba86ec1f8a3f532b16ac470e0

Speaker

Alberto Bressan, Penn State University, USA

Time

2020.11.10 10:00-11:00

Venue

Online—ZOOM APP

ZOOM Info

ZOOM Link
Conference ID: 920-119-02821
PIN Code: 729402

Abstract

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, where 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 presented, together with a new regularity result for optimal barriers, and an example where the optimal barrier can be explicitly computed.