Variational Methods in Shape Optimization Problems
Language: English
Published by Birkhäuser, 2005
Series: Book 22 of 53 - Progress in Nonlinear Differential Equations and Their Applications
- Hardcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
AbeBooks seller since August 14, 2006
Condition: New
£ 69.74
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Add to basketItem description from seller
Druck auf Anfrage Neuware - Printed after ordering - The fascinating eld of shape optimization problems has received a lot of attention in recent years, particularly in relation to a number of applications in physics and engineering that require a focus on shapes instead of parameters or functions. The goal of these applications is to deform and modify the admissible shapes in order to comply with a given cost function that needs to be optimized. In this respect the problems are both classical (as the isoperimetric problem and the Newton problem of the ideal aerodynamical shape show) and modern (re ecting the many results obtained in the last few decades). The intriguing feature is that the competing objects are shapes, i.e., domains of N R , instead of functions, as it usually occurs in problems of the calculus of va- ations. This constraint often produces additional dif culties that lead to a lack of existence of a solution and to the introduction of suitable relaxed formulations of the problem. However, in certain limited cases an optimal solution exists, due to the special form of the cost functional and to the geometrical restrictions on the class of competing domains.…
Seller Inventory # 9780817643591
- Title
- Variational Methods in Shape Optimization Problems
- Author
- Dorin Bucur
- Publisher
- Birkhäuser
- Publication year
- 2005
- Condition
- Neu
- Binding
- Buch
- Language
- English
- ISBN 10
- 0817643591
- ISBN 13
- 9780817643591
- Item weight
- 512 grams
- Dimensions
- 241x160x18 mm
- Series
- Book 22 of 53: Progress in Nonlinear Differential Equations and Their Applications
Shape optimization problems are treated from the classical and modern perspectives
Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems
Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis
Driven by several good examples and illustrations
Poses some open questions.
"Synopsis" may belong to another edition of this title.
From the Back Cover
The study of shape optimization problems encompasses a wide spectrum of academic research with numerous applications to the real world. In this work these problems are treated from both the classical and modern perspectives and target a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems.
Key topics and features:
* Presents foundational introduction to shape optimization theory
* Studies certain classical problems: the isoperimetric problem and the Newton problem involving the best aerodynamical shape, and optimization problems over classes of convex domains
* Treats optimal control problems under a general scheme, giving a topological framework, a survey of "gamma"-convergence, and problems governed by ODE
* Examines shape optimization problems with Dirichlet and Neumann conditions on the free boundary, along with the existence of classical solutions
* Studies optimization problems for obstacles and eigenvalues of elliptic operators
* Poses several open problems for further research
* Substantial bibliography and index
Driven by good examples and illustrations and requiring only a standard knowledge in the calculus of variations, differential equations, and functional analysis, the book can serve as a text for a graduate course in computational methods of optimal design and optimization, as well as an excellent reference for applied mathematicians addressing functional shape optimization problems.
"About the title" may belong to another edition of this title.
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