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 wellposed or illposed 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 NavierStokes equations. Readership Graduate students and research mathematicians interested in analysis, specifically calculus of variations and optimal control and optimization; physicists; engineers. Reviews "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 paraboliclike control problems with particular emphasis on NavierStokes equations. The proofs are complete and accessible to nonspecialists ... 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 NavierStokes equations
 The Cauchy problem for elliptic equations in a conditionally wellposed formulation
 The local exact controllability of the flow of incompressible viscous fluid
 Bibliography
 Index
