Hardcover ISBN:  9780821813829 
Product Code:  MMONO/187 
List Price:  $128.00 
MAA Member Price:  $115.20 
AMS Member Price:  $102.40 
Electronic ISBN:  9781470446017 
Product Code:  MMONO/187.E 
List Price:  $127.00 
MAA Member Price:  $114.30 
AMS Member Price:  $101.60 

Book DetailsTranslations of Mathematical MonographsVolume: 187; 2000; 305 ppMSC: Primary 93; Secondary 35; 76;
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.
ReadershipGraduate students and research mathematicians interested in analysis, specifically calculus of variations and optimal control and optimization; physicists; engineers.

Table of Contents

Chapters

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


Additional Material

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


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

Chapters

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

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