Variational Methods in Shape Optimization Problems
Dorin Bucur, Giuseppe Buttazzo - Collection Progress in Nonlinear Differential Equations and Their Applications
Résumé
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.
Sommaire
- Preface
- Introduction to Shape Optimization Theory and Some Classical Problems
- Optimization Problems over Classes of Convex Domains
- Optimal Control Problems: A General Scheme
- Shape Optimization Problems with Dirichlet Condition on the Free Boundary
- Existence of Classical Solutions
- Optimization Problems for Functions of Eigenvalues
- Shape Optimization Problems with Neumann Condition on the Free Boundary
- Bibliography
- Index
Caractéristiques techniques
PAPIER | |
Éditeur(s) | Birkhäuser |
Auteur(s) | Dorin Bucur, Giuseppe Buttazzo |
Collection | Progress in Nonlinear Differential Equations and Their Applications |
Parution | 31/12/2004 |
Nb. de pages | 216 |
Format | 16 x 24 |
Couverture | Relié |
Poids | 504g |
Intérieur | Noir et Blanc |
EAN13 | 9780817643591 |
ISBN13 | 978-0-8176-4359-1 |
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