Partial Differential Equations arising in light reflection & optimisation
主 题: Partial Differential Equations arising in light reflection & optimisation
报告人: Professor Xu-Jia Wang (Australian National University)
时 间: 2014-09-26 15:00-16:00
地 点: 理科一号楼 1114（数学所活动）
In this talk we consider a class of partial differential equations arising in the design of reflector antenna and optimal transportation. Given a light source and a surface to be illuminated, we want to design a reflector such that the output light covers the given surface. We show that this problem can be described by a complicated partial differential equation of Monge-Ampere type subject to a second boundary condition. We show that this problem is in fact an energy minimizing problem, which is also an optimisation problem and is related to the linear or nonlinear programming introduced by Kantorovich. This kind of optimisation problem was extensively studied in recent years. The energy functional enables us to find a weak solution to the problem. By studying the regularity of solutions to the associated Monge-Ampere equation, conditions on the smoothness of the reflector has also be established.