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Variational Methods in Shape Optimization Problems
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Variational Methods in Shape Optimization Problems

Variational Methods in Shape Optimization Problems

Dorin Bucur, Giuseppe Buttazzo - Collection Progress in Nonlinear Differential Equations and Their Applications

216 pages, parution le 31/12/2004

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
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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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