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＜図書＞
Optimal control of partial differential equations : theory, methods, and applications
| 責任表示 | Fredi Tröltzsch ; translated by Jürgen Sprekels |
|---|---|
| シリーズ | Graduate studies in mathematics ; v. 112 |
| データ種別 | 図書 |
| 出版情報 | Providence, R.I. : American Mathematical Society , c2010 |
| 本文言語 | 英語 |
| 大きさ | xv, 399 p. : ill. ; 27 cm |
| 概要 | "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 aero...autics, 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, TroÌltzsch 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.続きを見る |
| 目次 | 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. |
| 電子版へのリンク | https://hdl.handle.net/2324/6988810 |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
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理系図3F 数理独自 | TROL/10/2 | 2010 |
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033212010000748 |
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書誌詳細
| 別書名 | 原タイトル:Optimale Steuerung partieller Differentialgleichungen |
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| 一般注記 | Includes bibliographical references and index |
| 著者標目 | *Tröltzsch, Fredi, 1951- |
| 件 名 | LCSH:Control theory LCSH:Differential equations, Partial LCSH:Mathematical optimization |
| 分 類 | LCC:QA402.3 DC22:515/.642 |
| 書誌ID | 1001421055 |
| ISBN | 9780821849040 |
| NCID | BB01859990 |
| 巻冊次 | ISBN:9780821849040 |
| 登録日 | 2010.05.20 |
| 更新日 | 2017.02.18 |