Conference ID: 920-119-02821
PIN Code: 729402
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.
Prof. Alberto Bressan obtained his PhD in mathematics from University of Colorado in 1982. He became a full professor at the SISSA in Trieste, Italy in 1991. In 2003, he moved to Penn State University to assume a full professorship there — a position he still holds.
Prof. Bressan’s research interests include: hyperbolic systems of conservation laws and nonlinear wave equations, systems of Hamilton–Jacobi equations, discounted differential games, dynamic blocking problems, etc. He made important contributions to the well-posedness theory and vanishing viscosity limit for the hyperbolic conservation laws.
Prof. Bressan won the A. Feltrinelli prize for Mathematics, Mechanics and Applications of the Accademia Nazionale dei Lincei in Rome, the Analysis of Partial Differential Equations Prize of the SIAM in 2007, and the Bôcher Memorial Prize in 2008. He was appointed to the Eberly Family Chair in Mathematics at Penn State in 2008. In 2012 he was selected as a fellow of the American Mathematical Society. Prof. Bressan was the plenary speaker for the International Congress of Mathematicians in Beijing in 2002.