Variational Methods in Shape Optimizatio
β Dorin Bucur, Giuseppe Buttazzo
π Library
π
2005
π BirkhΓ€user Boston
π English
β¦ LIBER β¦
π
Variational Methods in Shape Optimization Problems
β Scribed by Dorin Bucur, Giuseppe Buttazzo (auth.)
- Publisher
- BirkhΓ€user Basel
- Year
- 2005
- Tongue
- English
- Leaves
- 217
- Series
- Progress in Nonlinear Differential Equations and Their Applications 65
- Edition
- 1
- Category
- Library
β¬ Acquire This Volume
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β¦ Synopsis
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.
β¦ Table of Contents
Introduction to Shape Optimization Theory and Some Classical Problems....Pages 1-29
Optimization Problems over Classes of Convex Domains....Pages 31-52
Optimal Control Problems: A General Scheme....Pages 53-74
Shape Optimization Problems with Dirichlet Condition on the Free Boundary....Pages 75-119
Existence of Classical Solutions....Pages 121-143
Optimization Problems for Functions of Eigenvalues....Pages 145-173
Shape Optimization Problems with Neumann Condition on the Free Boundary....Pages 175-203
β¦ Subjects
Calculus of Variations and Optimal Control; Optimization; Optimization; Partial Differential Equations; Functional Analysis; Difference and Functional Equations; Applications of Mathematics
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