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Differential Geometric Methods in the Control of Partial Differential Equations
Edited by: Robert Gulliver and Walter Littman, University of Minnesota, Minneapolis, MN, and Roberto Triggiani, University of Virginia, Charlottesville, VA
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Contemporary Mathematics
2000; 406 pp; softcover
Volume: 268
ISBN-10: 0-8218-1927-5
ISBN-13: 978-0-8218-1927-2
List Price: US$91
Member Price: US$72.80
Order Code: CONM/268
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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.

Readership

Graduate students and research mathematicians interested in differential geometry.

Table of Contents

  • G. Avalos -- Wellposedness of a structural acoustics model with point control
  • J. Cagnol and J.-P. Zolésio -- Intrinsic geometric model for the vibration of a constrained shell
  • M. Camurdan and G. Ji -- A noise reduction problem arising in structural acoustics: A three-dimensional solution
  • S. Chanillo, D. Grieser, and K. Kurata -- The free boundary problem in the optimization of composite membranes
  • M. C. Delfour -- Tangential differential calculus and functional analysis on a \(C^{1,1}\) submanifold
  • M. M. Eller and V. Isakov -- Carleman estimates with two large parameters and applications
  • J. F. Escobar -- On the prescribed Scalar curvature problem on compact manifolds with boundary
  • R. Gulliver and W. Littman -- Chord uniqueness and controllability: The view from the boundary, I
  • M. A. Horn -- Nonlinear boundary stabilization of a system of anisotropic elasticity with light internal damping
  • V. Isakov and M. Yamamoto -- Carleman estimate with the Neumann boundary condition and its applications to the observability inequality and inverse hyperbolic problems
  • I. Lasiecka, R. Triggiani, and X. Zhang -- Nonconservative wave equations with unobserved Neumann B. C.: Global uniqueness and observability in one shot
  • C. Lebiedzik -- Uniform stability of a coupled structural acoustic system with thermoelastic effects and weak structural damping
  • T. Lewiński and J. Sokołowski -- Topological derivative for nucleation of non-circular voids. The Neumann problem
  • W. Littman -- Remarks on global uniqueness theorems for partial differential equations
  • Z. Slodkowski and G. Tomassini -- Evolution of a graph by Levi form
  • P.-F. Yao -- Observability inequalities for the Euler-Bernoulli plate with variable coefficients
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