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Exact controllability for a refined stochastic wave equation
时间:2024年07月10日 09:26 点击数:

报告人:吕琦

报告地点:数学与统计学院二楼会议室

报告时间:2024年07月11日星期四09:30-10:30

邀请人:冀书关

报告摘要:

A widely used stochastic wave equation is the classical wave equation perturbed by a term of It^o’s integral. We show that this equation is not exactly controllable even if the controls are effective everywhere in both the drift and the diffusion terms and also on the boundary. In some sense this means that some key feature has been ignored in this model. Then, based on a stochastic Newton’s law, we propose a refined stochastic wave equation. By means of a new global Carleman estimate, we establish the exact controllability of our stochastic wave equation with three controls. Moreover, we give a result about the lack of exact controllability, which shows that the action of three controls is necessary. Our analysis indicates that, at least from the point of view of control theory, the new stochastic wave equation introduced in this paper is a more reasonable model than that in the existing literatures.

主讲人简介:

吕琦,四川大学数学学院教授,博士生导师,高层次领军人才,国际数学家大会报告人。主要研究偏微分方程和随机微分方程的控制理论,做出了系列开创性工作,于Communications on Pure and Applied Mathematics、Journal of the European Mathematical Society、Journal de Mathématiques Pures et Appliquées、SIAM Journal on Control and Optimization、 Journal of Functional Analysis、Journal of Differential Equations和Inverse Problems等发表论文多篇,并在Springer-Verlag出版专著二部,曾于2013年获中国数学会钟家庆奖,2018年获中国工业与应用数学学会应用数学青年科技奖,并担任SIAM Journal on Control and Optimization, ESAIM: Control, Optimisation and Calculus of Variations和Systems & Control Letters等刊物的编委。

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