题目：Exact Controllability of the Lazer-McKenna suspension bridge equation
摘要: It is well known that suspension bridges may display certain oscillations under external aerodynamic forces. Based upon the fundamental nonlinearity in suspension bridges that the stays connecting the supporting cables and the roadbed resist expansion, but do not resist compression, new models describing oscillations in suspension bridges were developed by Lazer and McKenna in 1990's. In the existing literatures, there have been very few work on controls of the Lazer-McKenna suspension bridge models.
In this talk, I will present some of our recent work on exact controllability of the Lazer McKenna suspension bridge equation with a locally distributed control. Unlike most of the existing literatures on exact controllability of nonlinear systems, the nonlinearity in the Lazer-McKenna suspension bridge equation is not differentiable, which makes the exactcontrollability problem challenging to study. By using the Hilbert Uniqueness Method and the Leray-Schauder degree theory, we prove that the control system is exactly controllable.
A key step is to establish the observability inequality of an auxiliary linear control problem. The proof of such an inequality relies on deriving a Carleman estimate.
腾讯会议号：937 778 957
简介：丁中海是美国内华达大学拉斯维加斯分校数学科学系教授、博士生导师，曾长期负责数学系的研究生工作。他感兴趣的领域有Control theory，Partial differential equation, Mathematical Modeling，Numerical computation等，在 SIAM JMA, CPA, JMP, JCAM等国际重要期刊上发表论文数十篇。