Variational Methods in Shape Optimization Problems
By: Bucur, Dorin [author.].
Contributor(s): Buttazzo, Giuseppe [author.2] | SpringerLink (Online service)0.
Material type:
BookSeries: Progress in Nonlinear Differential Equations and Their Applications ; 650.Publisher: Boston, MA : Birkh�user Boston, 2005. Description: VIII, 216 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780817644031.Subject(s): Mathematics | Difference equations | Functional equations | Functional analysis | Partial differential equations | Applied mathematics | Engineering mathematics | Mathematical optimization | Calculus of variations.1 | Mathematics.2 | Calculus of Variations and Optimal Control; Optimization.2 | Optimization.2 | Partial Differential Equations.2 | Functional Analysis.2 | Difference and Functional Equations.2 | Applications of Mathematics.1DDC classification: 515.64 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
| PK Kelkar Library, IIT Kanpur | Available | EBK6320 |
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.
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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