“数理论坛”第102期：1. Reconstruction of initial data for parabolic equations 2. Characterization of stabilization by observability inequalities of stabilization

报告题目

1. Reconstruction of initial data for parabolic equations

2. Characterization of stabilization by observability inequalities of stabilization

报告时间

2019年8月3日（周六）上午9:00-12:00

报告地点

东区综合教学楼A座1404

报告人

Kim-Dang Phung教授，汪更生教授

报告人

简介

Kim-Dang Phung，法国University of Orleans大学教授，从事偏微分方程及其控制理论的研究，在Journal of the European Mathematical Society， SIAM J. Control Optim.，Journal of Functional Analysis等国际重要期刊上发表论文近三十篇；

汪更生，天津大学应用数学中心教授. 主要从事分布参数系统控制理论的研究，出版《Time Optimal Control of Evolution Equations》、《Periodic Feedback Stabilization for Linear Periodic Evolution Equations》学术专著两部. 现任国际控制论权威刊物《SIAM J. Control Optim.》以及控制论知名期刊《ESAIM Control Optim. Calc. Var.》和《Mathematical Control and Related Fields》的编委.

报告摘要

1.In this talk, we establish a formula to recover the initial data for a parabolic equation from the knowlegde of the soluton at a future time restricted to a subset in space. The tools used are: eigenfunction expansion, impulse control theory, regularization of inverse problem and estimate of unique continuaion. We will show how to organize these tools to get the desired formula.

2. Given a linear control system in a Hilbert space with a bounded control operator, we establish a characterization of exponential stabilizability in terms of an observability inequality. In general, characterizations of stabilization are presented by certain frequency conditions which are in "fequency domain". Our characterization is given in "time domain". The way to approach the aim is as: we realize that the exponential stabilization is equivalent to a special kind of controllability, and then by the duality argument, it is equivalent to a weak observability inequality.

邀请人

刘汉兵 副教授

2019年7月29日