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