Variational Methods in Shape Optimization Problems
Summary
The feel-good place to buy books
Variational Methods in Shape Optimization Problems by Dorin Bucur
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.From the reviews:
"The book under review deals with some variational methods to treat shape optimization problems …The book contains a complete study of mathematical problems for scalar equations and eigenvalues, in particular regarding the existence of solutions in shape optimization. … The main goal of the book is to focus on the existence of an optimal shape, necessary conditions of optimality, and stability of optimal solutions under some prescribed kind of perturbations." (Jan Sokolowski, Mathematical Reviews, Issue 2006 j)
“The authors predominantly analyze optimal shape and optimal control problems … . The book, though slim, is rich in content and provides the reader with a wealth of information, numerous analysis and proof techniques, as well as useful references (197 items). … Numerous nontrivial examples illustrate the theory and can please even those readers who are rather application-oriented.” (Jan Chleboun, Applications of Mathematics, Vol. 55 (5), 2010)
| SKU | NIN9780817643591 |
| ISBN 13 | 9780817643591 |
| ISBN 10 | 0817643591 |
| Title | Variational Methods in Shape Optimization Problems |
| Author | Dorin Bucur |
| Series | Progress In Nonlinear Differential Equations And Their Applications |
| Condition | New |
| Publisher | Birkhauser Boston Inc |
| Year published | 2005-07-01 |
| Number of pages | 216 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | This is a new book - be the first to read this copy. With untouched pages and a perfect binding, your brand new copy is ready to be opened for the first time |
