| Optimization of Elliptic Systems: Theory and Applications 2006 Edition Contributor(s): Neittaanmaki, Pekka (Author), Sprekels, Jürgen (Author), Tiba, Dan (Author) |
|
 |
ISBN: 0387272356 ISBN-13: 9780387272351 Publisher: Springer OUR PRICE: $161.49 Product Type: Hardcover - Other Formats Published: December 2005 Annotation: This monograph provides a comprehensive and accessible introduction to the optimization of elliptic systems. This area of mathematical research, which has many important application in science and technology, has experienced an impressive development during the last two decades. This monograph aims to address some of the pressing unsolved questions in the field. The exposition concentrates along two main directions: the optimal control of linear and nonlinear elliptic equations, and problems involving unknown and/or variable domains. Throughout this monograph, the authors elucidate connections between seemingly different types of problems. One basic feature is to relax the needed regularity assumptions as much as possible in order to include larger classes of possible applications. The book is organized into six chapters that give a gradual and accessible presentation of the material, and a special effort is made to present numerous examples. This monograph is addressed to a large readership, primarily to graduate students and researchers working in this field of mathematics. Much of this material will prove useful also for scientists from other fields where the optimization of elliptic systems occurs, such as physics, mechanics, and engineering. |
| Additional Information |
| BISAC Categories: - Technology & Engineering - Mathematics | Linear & Nonlinear Programming - Mathematics | Differential Equations - General |
| Dewey: 609.41 |
| LCCN: 2006295670 |
| Series: Springer Monographs in Mathematics |
| Physical Information: 1.11" H x 6.36" W x 9.62" (1.87 lbs) 512 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: The present monograph is intended to provide a comprehensive and accessible introduction to the optimization of elliptic systems. This area of mathematical research, which has many important applications in science and technology. has experienced an impressive development during the past two decades. There are already many good textbooks dealing with various aspects of optimal design problems. In this regard, we refer to the works of Pironneau 1984], Haslinger and Neittaanmaki 1988], 1996], Sokolowski and Zolksio 1992], Litvinov 2000], Allaire 2001], Mohammadi and Pironneau 2001], Delfour and Zolksio 2001], and Makinen and Haslinger 2003]. Already Lions I9681 devoted a major part of his classical monograph on the optimal control of partial differential equations to the optimization of elliptic systems. Let us also mention that even the very first known problem of the calculus of variations, the brachistochrone studied by Bernoulli back in 1696. is in fact a shape optimization problem. The natural richness of this mathematical research subject, as well as the extremely large field of possible applications, has created the unusual situation that although many important results and methods have already been est- lished, there are still pressing unsolved questions. In this monograph, we aim to address some of these open problems; as a consequence, there is only a minor overlap with the textbooks already existing in the field. |