Shape Optimization and Free Boundaries

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.

Auteur

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.

Contenu

Preface. Free Boundary Problems in Geochemistry; J. Chadam.(with an appendix by R. Ricci). Shape Derivatives and Differentiability of Min Max; M.C. Delfour. Some Free Boundary Problems with Industrial Applications; A. Fasano. Problèmes de surfaces libres en mécanique des fluides; M. Fortin. Numerical Structural Optimization via a Relaxed Formulation; R.V. Kohn. Optimal Shape Design with Applications to Aerodynamics; O. Pironneau. Approximation and Localization of Attractors; K. Promislow, R. Temam. Shape Sensitivity Analysis of Variational Inequalities; J. Sokolowski. Diffusion with Strong Absorption; I. Stakgold. An Introduction to the Mathematical Theory of the Porous Medium Equation; J.L. Vazquez. Asymptotic Behaviour Near Extinction Points for a Semilinear Equation with Strong Absorption; J.J.L. Velázquez. Introduction to Shape Optimization Problems and Free Boundary Problems; J.-P. Zolésio. Index.