报告题目：Exact Controllability for a Refined Stochastic Wave Equation

报 告 人：吕琦教授（四川大学）

报告时间：2024年5月10日  16:30-17:30

报告地点：格物楼528

报告摘要：

A widely used stochastic wave equation is the classical wave equation perturbed by a term of Ito'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.

报告人简介：

吕琦，四川大学数学学院教授，博士生导师，国家杰出青年科学基金获得者，世界数学家大会45分钟报告者。主要研究微分方程和随机微分方程的控制理论，尤其在随机偏微分方程极大值原理领域做出开创性工作，在CPAM、JEMS、JMPA、SICON等发表论文多篇，担任SICON等刊物编委。