报告人：Enrique Zuazua
报告地点：Zoom会议
报告时间：2020年12月05日星期六19:30-20:30
邀请人：高夯
报告摘要：
We shall discuss the inverse problem, or inverse design problem, for a time-evolution Hamilton--Jacobi equation and the 1-d analog in the context of scalar conservation laws. More precisely, given a target function and a time horizon, we aim to construct all the initial conditions for which the viscosity solution coincides the given target at the given time. As is common in this kind of nonlinear equation, the target might not be reachable. We first study the existence of at least one initial condition leading the system to the given target. The natural candidate, which indeed allows determining the reachability of the target , is the one obtained by reversing the direction of time in the equation. When is reachable, we construct the set of all the initial conditions for which the viscosity solutions lead to the final target.
We shall also discuss a number of open problems arising in this area and the possible link with other control problems through value functions, in particular in the context of reinforcement learning.
会议网址：https://zoom.com.cn/j/68688731751
会议ID：686 887 31751
会议密码：779192
主讲人简介：
Professor Enrique Zuazua， Chair in Applied Analysis-Alexander von Humboldt Professorship at FAU-Friedrich-Alexander University, Erlangen-Nürnberg (Germany). He has been awarded the Advanced Grants by the European Research Council (ERC) NUMERIWAVES in 2010 and DyCon in 2016.
Professor Zuazua is an Honorary member of the Academia Europaea and Jakiunde, the Basque Academy of Sciences, Letters and Humanities, Doctor Honoris Causa from the Université de Lorraine in France and Ambassador of the Friedrisch-Alexandre University in Erlangen-Nurenberg, Germany. He was an invited speaker at ICM2006 in the section on Control and Optimization.
His fields of expertise in the area of Applied Mathematics cover topics related with Partial Differential Equations, Systems Control and Machine Learning, led to some fruitful collaboration in different industrial sectors such as the optimal shape design in aeronautics and the management of electrical and water distribution networks.
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