Optimization Methods in Partial Differential Equations
About this Title
Steven Cox and Irena Lasiecka, Editors
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.
Graduate students and research mathematicians interested in analytical and/or numerical methods in calculus of variations and in PDEs.
Table of Contents
- Fatiha Alabau and Vilmos Komornik – Boundary observability and controllability of linear elastodynamic systems [MR 1472283]
- Youcef Amirat and Jacques Simon – Riblets and drag minimization [MR 1472284]
- Giles Auchmuty – Min-max problems for non-potential operator equations [MR 1472285]
- Piermarco Cannarsa and Carlo Sinestrari – An infinite-dimensional time optimal control problem [MR 1472286]
- Bernard Dacorogna and Paolo Marcellini – Dirichlet problem for nonlinear first order partial differential equations [MR 1472287]
- Michel C. Delfour and Jean-Paul Zolésio – Hidden boundary smoothness for some classes of differential equations on submanifolds [MR 1472288]
- Michel C. Delfour and Jean-Paul Zolésio – Convergence to the asymptotic model for linear thin shells [MR 1472289]
- F. Fahroo and K. Ito – Variational formulation of optimal damping designs [MR 1472290]
- A. V. Fursikov and O. Yu. Imanuvilov – Local exact boundary controllability of the Navier-Stokes system [MR 1472291]
- Victor Isakov – On uniqueness and stability in the Cauchy problem [MR 1472292]
- K. Kunisch and S. Volkwein – Augmented Lagrangian-SQP techniques and their approximations [MR 1472293]
- John E. Lagnese – Recent progress and open problems in control of multi-link elastic structures [MR 1472294]
- Konstantin A. Lurie – Spatio-temporal control in the coefficients of linear hyperbolic equations [MR 1472295]
- Roman A. Polyak – Modified interior distance functions [MR 1472296]
- Bopeng Rao – Optimal energy decay rate in a damped Rayleigh beam [MR 1472297]
- David L. Russell – Approximate and exact formability of two-dimensional elastic structures; complete and incomplete actuator families [MR 1472298]
- Jan Sokołowski – Displacement derivatives in shape optimization of thin shells [MR 1472299]
- Daniel Tataru – Carleman estimates, unique continuation and controllability for anizotropic PDEs [MR 1472300]
- R. Temam and M. Ziane – Navier-Stokes equations in thin spherical domains [MR 1472301]
- R. Triggiani – The algebraic Riccati equation with unbounded control operator: the abstract hyperbolic case revisited [MR 1472302]
- M. I. Zelikin – One-parameter families of solutions to a class of PDE optimal control problems [MR 1472303]