NSF/CBMS Regional Conference in the Mathematical Sciences-Mathematical Control Theory of Coupled Systems of Partial Differential Equations 8/3/99-8/7/99

Irena Lasiecka教授将担任NSF-CBMS区域研究会议的首席讲师，会议主题是“偏微分方程组耦合系统的数学控制理论”。这一系列讲座的目的是提供一个独立的、全面的阐述，导致最先进的结果。研究偏微分方程组耦合系统的动机来自于工程中涉及结构/声学相互作用、大规模柔性结构、流体/结构相互作用等交互结构的各种技术进步。这些系统被描述为强耦合偏微分方程组，通常耦合在边界上，具有混合类型的动力学。耦合的影响阻碍了解耦方程的结果和技术的直接应用，因此需要开发新的技术，通常基于微局部分析和奇点传播。为了有效地集中注意力和传达主题的主要思想，讲座将集中在交互系统的特定基准模型上：结构声学相互作用；热/结构相互作用；复合板；动力壳；以及以上各项的组合。这些讲座将在数学控制理论的背景下对这些系统进行完整的分析，重点是三种类型的控制问题，它们是经典控制理论的基石：最优控制、可控性和稳定性。前四堂课将讨论分析相互作用结构所需的非耦合偏微分方程组理论的那些方面。剩下的六堂课将直接讨论互动结构。讲座的主题是：具有无界强迫项和边界输入的线性和非线性半群的理论；具有无界控制和观测的抽象控制理论；控制理论中的偏微分方程方法；交互结构的偏微分方程模型；交互结构的最优控制和优化问题；以及交互结构的可控性和稳定性。

Professor Irena Lasiecka will be the Principal Lecturer for an NSF-CBMS Regional Research Conference on ``Mathematical Control Theory of Coupled Systems of Partial Differential Equations.'' The aim of this lecture series is to provide a self-contained, comprehensive exposition leading up to state-of-the-art results. The motivation for the study of coupled systems of PDE's comes from a variety of technological advancements in engineering involving interactive structures such as structure/acoustic interactions, large scale flexible structures, fluid/structure interactions, etc. These systems are described by strongly coupled PDEs, often coupled on the boundary, with mixed types of dynamics. The effect of the coupling prevents the direct application of results and techniques for uncoupled equations, so new techniques need to be developed, often based on microlocal analysis and propagation of singularities.In order to effectively focus attention and convey the main ideas of the topic, the lectures will concentrate on specific benchmark models of interactive systems: structural acoustics interactions; thermal/structureinteractions; composite plates; dynamic shells; and combinations of the above. The lectures will provide a complete analysis of these systems in the context of mathematical control theory, focusing on three types of control problems which are the cornerstones of classical control theory: optimal control, controllability, and stabilization. The first four lectures will deal with those aspects of the theory of uncoupled PDE's which are required for the analysis of interactive structures. The remaining six lectures will deal directly with interactive structures. The lecture topics are: Theory of linear and nonlinear semigroups with unbounded forcing terms and boundary inputs; Abstract control theory with unbounded controls and observations; PDE methods in control theory; PDE models of interactive structures; Optimal control and optimization problems for interactive structures; and Controllability and stabilization of interactive structures.