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Shape Optimization and Free Boundaries

  • Book
  • © 1992

Overview

Editors:
  1. Michel C. Delfour

    1. Centre de recherches mathématiques, Université de Montréal, Montréal, Canada

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  2. Gert Sabidussi
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Part of the book series: Nato Science Series C: (ASIC, volume 380)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Free Boundary Problems in Geochemistry

    • John Chadam
    Pages 1-34

  3. Shape Derivatives and Differentiability of Min Max

    • Michel C. Delfour
    Pages 35-111

  4. Some Free Boundary Problems With Industrial Applications

    • Antonio Fasano
    Pages 113-142

  5. Problèmes de surfaces libres en mécanique des fluides

    • Michel Fortin
    Pages 143-171

  6. Numerical Structural Optimization via a Relaxed Formulation

    • Robert V. Kohn
    Pages 173-210

  7. Optimal Shape Design with Applications to Aerodynamics

    • Olivier Pironneau, I.N.R.I.A.
    Pages 211-251

  8. Approximation and Localization of Attractors

    • Keith Promislow, Roger Temam, Laboratoire d’Analyse Numérique
    Pages 253-285

  9. Shape sensitivity analysis of variational inequalities

    • Jan Sokolowski
    Pages 287-319

  10. Diffusion with Strong Absorption

    • Ivar Stakgold
    Pages 321-345

  11. An Introduction to the Mathematical Theory of the Porous Medium Equation

    • Juan Luis Vazquez
    Pages 347-389

  12. Asymptotic Behaviour Near Extinction Points for a Semilinear Equation with Strong Absorption

    • Juan J. L. Velázquez
    Pages 391-395

  13. Introduction to Shape Optimization Problems and Free Boundary Problems

    • J. P. Zolésio
    Pages 397-457

  14. Back Matter

    Pages 459-462
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Keywords

About this book

Shape optimization deals with problems where the design or control variable is no longer a vector of parameters or functions but the shape of a geometric domain. They include engineering applications to shape and structural optimization, but also original applications to image segmentation, control theory, stabilization of membranes and plates by boundary variations, etc.
Free and moving boundary problems arise in an impressingly wide range of new and challenging applications to change of phase. The class of problems which are amenable to this approach can arise from such diverse disciplines as combustion, biological growth, reactive geological flows in porous media, solidification, fluid dynamics, electrochemical machining, etc.
The objective and orginality of this NATO-ASI was to bring together theories and examples from shape optimization, free and moving boundary problems, and materials with microstructure which are fundamental to static and dynamic domain and boundary problems.

Editors and Affiliations

  • Centre de recherches mathématiques, Université de Montréal, Montréal, Canada

    Michel C. Delfour

About the editors

Professor Delfour received his B. Arts in 1962 from the Université de Montréal, his B. Elect. Eng. (Honours Course) from McGill University in 1966, his M.Sc. from Case Institute of Technology in 1968, and his Ph.D. in Mathematics from Case Western Reserve University in 1970.
He has worked on the analysis and control of delay and distributed parameter systems. His current research interest include Shape Optimization, Free Boundary Problems, Control and Stability of Large Flexible Space Structure and Numerical Analysis.

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