Neuware -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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 228 pp. Englisch.

Bestandsnummer des Verk�ufers 9780817643591

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Titel: Variational Methods in Shape Optimization Problems
Verlag: Birkh�user Boston, Birkh�user Boston Jul 2005
Erscheinungsjahr: 2005
Sprache: Englisch
ISBN-10: 0817643591
ISBN-13: 9780817643591
Einband: Buch
Zustand: Neu

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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.

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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.

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