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Optimization Methods in Partial Differential Equations
Edited by: Steven Cox, Rice University, Houston, TX, and Irena Lasiecka, University of Virginia, Charlottesville
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Contemporary Mathematics
1997; 349 pp; softcover
Volume: 209
ISBN-10: 0-8218-0604-1
ISBN-13: 978-0-8218-0604-3
List Price: US$84
Member Price: US$67.20
Order Code: CONM/209
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This book presents a collection of papers written by specialists in the field and devoted to the analysis of various aspects of optimization problems with a common focus on partial differential equation (PDE) models. These papers were presented at the AMS-SIAM 1996 Joint Summer Research Conference held at Mount Holyoke College, South Hadley, MA, in June 1996.

The problems considered range from basic theoretical issues in the calculus of variations--such as infinite dimensional Hamilton Jacobi equations, saddle point principles, and issues of unique continuation--to ones focusing on application and computation, where theoretical tools are tuned to more specifically defined problems. The last category of these problems include inverse/recovery problems in physical systems, shape optimization and shape design of elastic structures, control and optimization of fluids, boundary controllability of PDE's including applications to flexible structures, etc.

The papers selected for this volume are at the forefront of research and point to modern trends and open problems. This book will be a valuable tool not only to specialists in the field interested in technical details, but also to scientists entering the field who are searching for promising directions for research.

Readership

Graduate students and research mathematicians interested in analytical and/or numerical methods in calculus of variations and in PDEs.

Table of Contents

  • F. Alabau and V. Komornik -- Boundary observability and controllability of linear elastodynamic systems
  • Y. Amirat and J. Simon -- Riblets and drag minimization
  • G. Achmuty -- Min-max problems for nonpotential operator equations
  • P. Cannarsa and C. Sinestrari -- An infinite dimensional time optimal control problem
  • B. Dacorogna and P. Marcellini -- Dirichlet problem for nonlinear first order partial differential equations
  • M. C. Delfour and J.-P. Zolésio -- Hidden boundary smoothness for some classes of differential equations on submanifolds
  • M. C. Delfour and J.-P. Zolésio -- Convergence to the asymptotic model for linear thin shells
  • F. Fahroo and K. Ito -- Variational formulation of optimal damping designs
  • A. V. Fursikov and O. Y. Imanuvilov -- Local exact boundary controllability of the Navier-Stokes system
  • V. Isakov -- On uniqueness and stability in the Cauchy problem
  • K. Kunisch and S. Volkwein -- Augmented Lagrangian-SQP techniques and their approximations
  • J. E. Lagnese -- Recent progress and open problems in control of multi-link elastic structures
  • K. A. Lurie -- Spatio-temporal control in the coefficients of linear hyperbolic equations
  • R. A. Polyak -- Modified interior distance functions
  • B. Rao -- Optimal energy decay rate in a damped Rayleigh beam
  • D. L. Russell -- Approximate and exact formability of two-dimensional elastic structures; Complete and incomplete actuator families
  • J. Sokołowski -- Displacement derivatives in shape optimization of thin shells
  • D. Tataru -- Carleman estimates, unique continuation and controllability for anizotropic PDE's
  • R. Temam and M. Ziane -- Navier-Stokes equations in thin spherical domains
  • R. Triggiani -- The algebraic Riccati equation with unbounded control operator: The abstract hyperbolic case revisited
  • M. I. Zelikin -- One-parameter families of solutions to a class of PDE optimal control problems
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