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The Resource Optimal control of partial differential equations : theory, methods, and applications, Fredi Tröltzsch ; translated by Jürgen Sprekels

Optimal control of partial differential equations : theory, methods, and applications, Fredi Tröltzsch ; translated by Jürgen Sprekels

Label
Optimal control of partial differential equations : theory, methods, and applications
Title
Optimal control of partial differential equations
Title remainder
theory, methods, and applications
Statement of responsibility
Fredi Tröltzsch ; translated by Jürgen Sprekels
Creator
Subject
Language
  • eng
  • ger
  • eng
Summary
"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."--Publisher's description
Member of
Cataloging source
DLC
Illustrations
illustrations
Index
index present
LC call number
QA402.3
LC item number
.T71913 2010
Literary form
non fiction
Nature of contents
bibliography
Series statement
Graduate studies in mathematics :
Series volume
v. 112
Optimal control of partial differential equations : theory, methods, and applications, Fredi Tröltzsch ; translated by Jürgen Sprekels
Label
Optimal control of partial differential equations : theory, methods, and applications, Fredi Tröltzsch ; translated by Jürgen Sprekels
Publication
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Bibliography note
Includes bibliographical references and index
Contents
Introduction and examples -- Linear-quadratic elliptic control problems -- Linear-quadratic parabolic control problems -- Optimal control of semilinear elliptic equations -- Optimal control of semilinear parabolic equations -- Optimization problems in Banach spaces -- Supplementary results on partial differential equations
http://library.link/vocab/cover_art
https://contentcafe2.btol.com/ContentCafe/Jacket.aspx?Return=1&Type=S&Value=9780821849040&userID=ebsco-test&password=ebsco-test
Dimensions
26 cm.
http://library.link/vocab/discovery_link
{'f': 'http://opac.lib.rpi.edu/record=b3368833'}
Extent
xv, 399 p.
Isbn
9780821849040
Isbn Type
(alk. paper)
Lccn
2009037756
Other physical details
ill.
System control number
(OCoLC)441945348

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