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Optimal Control of Distributed Systems. Theory and Applications
A. V. Fursikov, Moscow State University, Russia

Translations of Mathematical Monographs
2000; 305 pp; hardcover
Volume: 187
ISBN-10: 0-8218-1382-X
ISBN-13: 978-0-8218-1382-9
List Price: US$127
Member Price: US$101.60
Order Code: MMONO/187
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This volume presents the analysis of optimal control problems for systems described by partial differential equations. The book offers simple and clear exposition of main results in this area. The methods proposed by the author cover cases where the controlled system corresponds to well-posed or ill-posed boundary value problems, which can be linear or nonlinear. The uniqueness problem for the solution of nonlinear optimal control problems is analyzed in various settings. Solutions of several previously unsolved problems are given. In addition, general methods are applied to the study of two problems connected with optimal control of fluid flows described by the Navier-Stokes equations.


Graduate students and research mathematicians interested in analysis, specifically calculus of variations and optimal control and optimization; physicists; engineers.


"This book offers simple and clear exposition of main results in this area ... solutions of several previously unsolved problems are given."

-- Zentralblatt MATH

"The results provided in this book are interesting and focused on parabolic-like control problems with particular emphasis on Navier-Stokes equations. The proofs are complete and accessible to non-specialists ... provides a very good source of information for researchers ... can also be used as a graduate level textbook for students entering the field."

-- Mathematical Reviews

Table of Contents

  • The existence of solutions to optimal control problems
  • Optimality system for optimal control problems
  • The solvability of boundary value problems for a dense set of data
  • The problem of work minimization in accelerating still fluid to a prescribed velocity
  • Optimal boundary control for nonstationary problems of fluid flow and nonhomogeneous boundary value problems for the Navier-Stokes equations
  • The Cauchy problem for elliptic equations in a conditionally well-posed formulation
  • The local exact controllability of the flow of incompressible viscous fluid
  • Bibliography
  • Index
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