An error was encountered while trying to add the item to the cart. Please try again.
Copy To Clipboard
Successfully Copied!
Optimal Control of Partial Differential Equations: Theory, Methods and Applications

Fredi Tröltzsch Technische Universität Berlin, Berlin, Germany
Translated by Jürgen Sprekels
Available Formats:
Hardcover ISBN: 978-0-8218-4904-0
Product Code: GSM/112
List Price: $78.00 MAA Member Price:$70.20
AMS Member Price: $62.40 Electronic ISBN: 978-1-4704-1174-9 Product Code: GSM/112.E List Price:$73.00
MAA Member Price: $65.70 AMS Member Price:$58.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $117.00 MAA Member Price:$105.30
AMS Member Price: $93.60 Click above image for expanded view Optimal Control of Partial Differential Equations: Theory, Methods and Applications Fredi Tröltzsch Technische Universität Berlin, Berlin, Germany Translated by Jürgen Sprekels Available Formats:  Hardcover ISBN: 978-0-8218-4904-0 Product Code: GSM/112  List Price:$78.00 MAA Member Price: $70.20 AMS Member Price:$62.40
 Electronic ISBN: 978-1-4704-1174-9 Product Code: GSM/112.E
 List Price: $73.00 MAA Member Price:$65.70 AMS Member Price: $58.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$117.00 MAA Member Price: $105.30 AMS Member Price:$93.60
• Book Details

Volume: 1122010; 399 pp
MSC: Primary 49; 35; 90;

Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines.

This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces.

The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book self-contained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students.

Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers.

Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization.

Graduate students and research mathematicians interested in optimal control theory and PDEs.

• Chapters
• Chapter 1. Introduction and examples
• Chapter 2. Linear-quadratic elliptic control problems
• Chapter 3. Linear-quadratic parabolic control problems
• Chapter 4. Optimal control of semilinear elliptic equations
• Chapter 5. Optimal control of semilinear parabolic equations
• Chapter 6. Optimization problems in Banach spaces
• Chapter 7. Supplementary results on partial differential equations

• Reviews

• The book provides a thorough and self-contained introduction...[It includes] carefully chosen examples...The presentation of the material is clear and self-contained. A great deal of attention is paid to careful exposition of relevant supporting tools from nonlinear analysis and PDEs. ...A wealth of examples... [T]his is a very carefully written text with an eye on graduate students wishing to enter the field of PDE optimal control. The material presented is fairly complete, self-contained and well exposed.

Irena Lasiecka, Mathematical Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1122010; 399 pp
MSC: Primary 49; 35; 90;

Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines.

This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces.

The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book self-contained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students.

Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers.

Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization.

Graduate students and research mathematicians interested in optimal control theory and PDEs.

• Chapters
• Chapter 1. Introduction and examples
• Chapter 2. Linear-quadratic elliptic control problems
• Chapter 3. Linear-quadratic parabolic control problems
• Chapter 4. Optimal control of semilinear elliptic equations
• Chapter 5. Optimal control of semilinear parabolic equations
• Chapter 6. Optimization problems in Banach spaces
• Chapter 7. Supplementary results on partial differential equations
• The book provides a thorough and self-contained introduction...[It includes] carefully chosen examples...The presentation of the material is clear and self-contained. A great deal of attention is paid to careful exposition of relevant supporting tools from nonlinear analysis and PDEs. ...A wealth of examples... [T]his is a very carefully written text with an eye on graduate students wishing to enter the field of PDE optimal control. The material presented is fairly complete, self-contained and well exposed.

Irena Lasiecka, Mathematical Reviews
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
You may be interested in...
Please select which format for which you are requesting permissions.