TY - BOOK ID - 38294936 TI - Variational methods in shape optimization problems AU - Bucur, Dorin AU - Buttazzo, Giuseppe PY - 2005 VL - 65 SN - 9780817644031 9780817643591 0817643591 0817644032 PB - Boston (Mass.): Birkhäuser, DB - UniCat KW - Computer. Automation KW - automatisering KW - toegepaste wiskunde KW - Functional analysis KW - Mathematics KW - differentiaalvergelijkingen KW - kansrekening KW - wiskunde KW - Operational research. Game theory KW - Partial differential equations KW - functies (wiskunde) KW - Mathematical optimization KW - Shapes KW - Optimisation mathématique KW - Formes KW - EPUB-LIV-FT SPRINGER-B LIVMATHE KW - Mathematical optimization. KW - Shapes. KW - Differential equations, partial. KW - Functional analysis. KW - Functional equations. KW - Mathematics. KW - Calculus of Variations and Optimal Control; Optimization. KW - Optimization. KW - Partial Differential Equations. KW - Functional Analysis. KW - Difference and Functional Equations. KW - Applications of Mathematics. KW - Optimization (Mathematics) KW - Optimization techniques KW - Optimization theory KW - Systems optimization KW - Mathematical analysis KW - Maxima and minima KW - Operations research KW - Simulation methods KW - System analysis KW - Math KW - Science KW - Equations, Functional KW - Functional calculus KW - Calculus of variations KW - Functional equations KW - Integral equations KW - Calculus of variations. KW - Partial differential equations. KW - Difference equations. KW - Applied mathematics. KW - Engineering mathematics. KW - Calculus of differences KW - Differences, Calculus of KW - Equations, Difference KW - Isoperimetrical problems KW - Variations, Calculus of KW - Engineering KW - Engineering analysis KW - Differential equations, Partial. UR - https://www.unicat.be/uniCat?func=search&query=sysid:38294936 AB - 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. ER -