Ebook: 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.

---

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.

---

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.

Content:
Front Matter....Pages i-xviii
Free Boundary Problems in Geochemistry....Pages 1-34
Shape Derivatives and Differentiability of Min Max....Pages 35-111
Some Free Boundary Problems With Industrial Applications....Pages 113-142
Probl?mes de surfaces libres en m?canique des fluides....Pages 143-171
Numerical Structural Optimization via a Relaxed Formulation....Pages 173-210
Optimal Shape Design with Applications to Aerodynamics....Pages 211-251
Approximation and Localization of Attractors....Pages 253-285
Shape sensitivity analysis of variational inequalities....Pages 287-319
Diffusion with Strong Absorption....Pages 321-345
An Introduction to the Mathematical Theory of the Porous Medium Equation....Pages 347-389
Asymptotic Behaviour Near Extinction Points for a Semilinear Equation with Strong Absorption....Pages 391-395
Introduction to Shape Optimization Problems and Free Boundary Problems....Pages 397-457
Back Matter....Pages 459-462

---

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.

Content:
Front Matter....Pages i-xviii
Free Boundary Problems in Geochemistry....Pages 1-34
Shape Derivatives and Differentiability of Min Max....Pages 35-111
Some Free Boundary Problems With Industrial Applications....Pages 113-142
Probl?mes de surfaces libres en m?canique des fluides....Pages 143-171
Numerical Structural Optimization via a Relaxed Formulation....Pages 173-210
Optimal Shape Design with Applications to Aerodynamics....Pages 211-251
Approximation and Localization of Attractors....Pages 253-285
Shape sensitivity analysis of variational inequalities....Pages 287-319
Diffusion with Strong Absorption....Pages 321-345
An Introduction to the Mathematical Theory of the Porous Medium Equation....Pages 347-389
Asymptotic Behaviour Near Extinction Points for a Semilinear Equation with Strong Absorption....Pages 391-395
Introduction to Shape Optimization Problems and Free Boundary Problems....Pages 397-457
Back Matter....Pages 459-462
....