題目：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.
時間：2020年1月6日14：00
騰訊會議號：937 778 957
主講人：丁中海，內華達大學拉斯維加斯分校數學系教授
簡介：丁中海是美國內華達大學拉斯維加斯分校數學科學系教授、博士生導師，曾長期負責數學系的研究生工作。他感興趣的領域有Control theory，Partial differential equation, Mathematical Modeling，Numerical computation等，在 SIAM JMA, CPA, JMP, JCAM等國際重要期刊上發表論文數十篇。
