Stability and Control on a Model in Fluid-Structure Interaction
作者单位：Departamento de MatemáticasFacultad de CienciasUniversidad Autónoma de MadridMadridSpain28049
会议名称：《第二十二届中国控制会议》
会议日期：2003年
学科分类：0711[理学-系统科学] 07[理学] 08[工学] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 071102[理学-系统分析与集成] 081103[工学-系统工程]
基 金：Supported by the Grant BFM2002-03345 of the Spanish MCYT the Foundation for the Author of National Excellent Doctoral Dissertation of China (Project No: 200119) the EU TMR Projects Homogenization and Multiple Scales" and "Smart Systems"
关 键 词：Fluid-structure interaction coupled heat-wave system compact decoupling technique polynomial decay boundary control and observability
摘 要：正We consider a linearized and simplified model for fluid-structure interaction. The domain where the system evolves consists in two parts in which the wave and heat equations are satisfied respectively, with transmission conditions at the interface. First of all, based on a compact decoupling technique, we show that the solutions of the system do not decay exponentially. Next, by means of a careful spectral asymptotic analysis on high frequencies, we obtain the sharp polynomial decay rate of smooth solutions. Then, by combining sidewise energy estimates for the wave equation and Carleman inequalities for the heat one, we show the observability/null -controllability of the system with observation/control through the wave component. Finally, we prove the null-controllability of the system when the control acts on the boundary where the heat equation holds. The proof is based on a new Inghamtype inequality, which follows from the spectral analysis we develop and the observability inequality we get in the case that the observation is made through the wave component.