Free and moving boundaries: Analysis, simulation and control

Roland Glowinski, Jean-Paul Zolesio1584886064, 9781584886068, 9781420011159

Addressing algebraic problems found in biomathematics and energy, Free and Moving Boundaries: Analysis, Simulation and Control discusses moving boundary and boundary control in systems described by partial differential equations (PDEs). With contributions from international experts, the book emphasizes numerical and theoretical control of moving boundaries in fluid structure couple systems, arteries, shape stabilization level methods, family of moving geometries, and boundary control.
Using numerical analysis, the contributors examine the problems of optimal control theory applied to PDEs arising from continuum mechanics. The book presents several applications to electromagnetic devices, flow, control, computing, images analysis, topological changes, and free boundaries. It specifically focuses on the topics of boundary variation and control, dynamical control of geometry, optimization, free boundary problems, stabilization of structures, controlling fluid-structure devices, electromagnetism 3D, and inverse problems arising in areas such as biomathematics.
Free and Moving Boundaries: Analysis, Simulation and Control explains why the boundary control of physical systems can be viewed as a moving boundary control, empowering the future research of select algebraic areas.

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Table of contents :
1584886064……Page 1
Preface……Page 8
About the Editors……Page 10
Contributors……Page 12
Contents……Page 16
CHAPTER 1. Optimal tubes: Geodesic metric, Euler flow, and moving domain……Page 20
CHAPTER 2. Numerical simulation of pattern formation in a rotating suspension of non-Browniam settling particles……Page 56
CHAPTER 3. On the homogenization of optimal control problems on periodic graphs……Page 74
CHAPTER 4. Lift and sedimentation of particles in the flow of a viscoelastic liquid in a channel……Page 94
CHAPTER 5. Modeling and simulation of liquid-gas free surface flows……Page 130
CHAPTER 6. Transonic regular reflection for the unsteady transonic small disturbance equation-details of the subsonic solution……Page 144
CHAPTER 7. Shape optimization for 3D electrical impedance tomography……Page 184
CHAPTER 8. Analysis for the shape gradient in inverse scattering……Page 204
CHAPTER 9. Array antenna optimization……Page 222
CHAPTER 10. The Stokes basis for three-dimensional incompressible flow fields……Page 234
CHAPTER 11. Nonlinear aerolasticity, continuum theory, flutter/divergence speed, plate wing model……Page 242
CHAPTER 12. Differential Riccati equations for the Bolza problem associated with point boundary control of singular estimate control systems……Page 264
CHAPTER 13. Energy decay rates for the semiliear wave equation with nonlinear localized damping and source terms-an intrinsic approach……Page 282
CHAPTER 14. Electromagnetic 3D reconstruction by level set with zero capacity connecting sets……Page 300
CHAPTER 15. Shape and geometric methods in image processing……Page 312
CHAPTER 16. Topological derivatives for contact problems……Page 328
CHAPTER 17. The computing zoom……Page 340
CHAPTER 18. An optimization approach for the delamination of a composite material with nonpenetration……Page 350
CHAPTER 19. Adaptive refinement techniques in homogenization design method……Page 368
CHAPTER 20. Nonlinear stability of the flat-surface state in a Faraday experiment……Page 382
CHAPTER 21. A dynamic programming approach in Hilbert spaces for a family of applied delay optimal control problems……Page 394
CHAPTER 22. A posteriori error estimates of recovery type for a parameter estimation problem in a linear elastic problem……Page 414
CHAPTER 23. Tube derivative of noncylindrical shape functionals and variational formulations……Page 430
CHAPTER 24. A stochastic Riccati equation for a hyperbolic-like system with point and boundary control……Page 462