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

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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.