This volume contains selected papers that were presented at the AMS-IMS-SIAM Joint Summer Research Conference on ""Differential Geometric Methods in the Control of Partial Differential Equations"", which was held at the University of Colorado in Boulder in June 1999. The aim of the conference was to explore the infusion of differential-geometric methods into the analysis of control theory of partial differential equations, particularly in the challenging case of variable coefficients, where the physical characteristics of the medium vary from point to point. While a mutually profitable link has been long established, for at least 30 years, between differential geometry and control of ordinary differential equations, a comparable relationship between differential geometry and control of partial differential equations (PDEs) is a new and promising topic.Very recent research, just prior to the Colorado conference, supported the expectation that differential geometric methods, when brought to bear on classes of PDE modelling and control problems with variable coefficients, will yield significant mathematical advances. The papers included in this volume - written by specialists in PDEs and control of PDEs as well as by geometers - collectively support the claim that the aims of the conference are being fulfilled. In particular, they endorse the belief that both subjects - differential geometry and control of PDEs - have much to gain by closer interaction with one another. Consequently, further research activities in this area are bound to grow.
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978-0-8218-1927-2 (9780821819272)
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Schweitzer Klassifikation
Wellposedness of a structural acoustics model with point control by G. Avalos Intrinsic geometric model for the vibration of a constrained shell by J. Cagnol and J.-P. Zolesio A noise reduction problem arising in structural acoustics: A three-dimensional solution by M. Camurdan and G. Ji The free boundary problem in the optimization of composite membranes by S. Chanillo, D. Grieser, and K. Kurata Tangential differential calculus and functional analysis on a $C^{1,1}$ submanifold by M. C. Delfour Carleman estimates with two large parameters and applications by M. M. Eller and V. Isakov On the prescribed Scalar curvature problem on compact manifolds with boundary by J. F. Escobar Chord uniqueness and controllability: The view from the boundary, I by R. Gulliver and W. Littman Nonlinear boundary stabilization of a system of anisotropic elasticity with light internal damping by M. A. Horn Carleman estimate with the Neumann boundary condition and its applications to the observability inequality and inverse hyperbolic problems by V. Isakov and M. Yamamoto Nonconservative wave equations with unobserved Neumann B. C.: Global uniqueness and observability in one shot by I. Lasiecka, R. Triggiani, and X. Zhang Uniform stability of a coupled structural acoustic system with thermoelastic effects and weak structural damping by C. Lebiedzik Topological derivative for nucleation of non-circular voids. The Neumann problem by T. Lewinski and J. Sokolowski Remarks on global uniqueness theorems for partial differential equations by W. Littman Evolution of a graph by Levi form by Z. Slodkowski and G. Tomassini Observability inequalities for the Euler-Bernoulli plate with variable coefficients by P.-F. Yao.
