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Papers by jean-paul zolesio
Journal of Differential Equations, Dec 1, 2015
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Computer Methods in Applied Mechanics and Engineering, Aug 1, 1985
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IFAC Proceedings Volumes, Jul 1, 1984
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Springer eBooks, Sep 19, 2008
In this paper, we use the concept of connecting tubes introduced in [7][5] and we consider the ge... more In this paper, we use the concept of connecting tubes introduced in [7][5] and we consider the geodesic tube construction between two sets according to the tube shape metric. The first section is devoted to the tube analysis and formulation associated to the Galerkin-Level Set strategy. This new variational formulation consists in parameterizing the level set function in a finite vector space. Consequently, the aim of a Galerkin-Level Set method is more focused on topology that on high accuracy for the boundary approximation. However, the main advantage of this method, over the traditional level set formulation, concerns the standard partial differential equation (PDE) evolution for the level set function that, in the Galerkin-Level Set method turns into a system of ordinary differential equations and we avoid any “usual” instability. The second section concerns a shape identification problem associated to an Hilbert space metric using the Galerkin-Level Set method. In the last section, the geodesic tube construction is made by a optimization process based on a shape gradient calculus. Finally, a geodesic tube construction between two sets is validated by numerical experiments in 3D.
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Inverse Problems, 1999
ABSTRACT We are interested in a dynamical shape control problem in hydrodynamics. The considered ... more ABSTRACT We are interested in a dynamical shape control problem in hydrodynamics. The considered cost functional is the kinetic energy of a perfect and incompressible fluid. We establish the existence of a non-autonomous vector field which constructs the tube followed by the fluid in such a way as to minimize its kinetic energy. By introducing a specific adjoint state closely related to the shape of the tube, we derive the necessary optimality condition.
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Journal of Functional Analysis, Feb 1, 1992
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Siam Journal on Control and Optimization, Jul 1, 1988
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Springer eBooks, 1990
Recent work on the scole model.- Mathematical study of large space structures.- Symbolic formulat... more Recent work on the scole model.- Mathematical study of large space structures.- Symbolic formulation of dynamic equations for interconnected flexible bodies: The GEMMES software.- Adaptive optics - Shape control of an adaptive mirror.- Energy decay estimates for a beam with nonlinear boundary feedback.- Uniform stabilization of the wave equation with dirichlet-feedback control without geometrical conditions.- Actuators and controllability of distributed systems.- Linear quadratic control problem without stabilizability.- Riccati equations in noncylindrical domains.- Boundary control problems for non-autonomous parabolic systems.- Existence and optimal control for wave equation in moving domain.- Galerkine approximation for wave equation in moving domain.- Further results on exact controllability of the Euler-Bernoulli equation with controls on the dirichlet and neumann boundary conditions.- Some properties of the value function of a nonlinear control problem in infinite dimensions.- Identification of coefficients with bounded variation in the wave equation.- Shape hessian by the velocity method: A Lagrangian approach.- Shape sensitivity analysis of hyperbolic problems.- Differential stability of perturbed optimization with applications to parameter estimation.- A numerical method for drag minimization via the suction and injection of mass through the boundary.- Using the physical properties of systems for control: An illustration.
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Control of an overhead crane: Stabilization of flexibilities.- Exact controllability for linear d... more Control of an overhead crane: Stabilization of flexibilities.- Exact controllability for linear dynamic systems with skew symmetric operators.- Boundary homogenization and boundary shape optimization for a cylinder.- Relaxed formulation for a class of shape optimization problems.- On the smoothness of the value function along optimal trajectories.- Some boundary control problems and computation for the linear elastostatic kirchhoff plate on an exterior domain.- Approximate controllability for the wave equation.- Truss structures: Fourier conditions and eigenvalue problem.- Boundary control and stabilization of the one-dimensional wave equation.- Boundary control for inverse free boundary problems.- Differentiability of Min Max and saddle points under relaxed assumptions.- New noniterative approximations to the old riccati differential equation.- Numerical approach to the exact controllability of hyperbolic systems.- Shape sensitivity analysis for stochastic evolution equations.- Boundary controllability problems for the wave and heat equations.- About critical points of the energy in an electromagnetic shaping problem.- Finite dimesional compensator for flexible structures.- Remarks on boundary control for polyhedral domains and related results.- Stability of the travelling waves in a class of free boundary problems arising in combustion theory.- A convergent finite element scheme for a wave equation with a moving boundary.- A boundary controllability approach in optimal shape design problems.- Regularity with interior point control. Part I: Wave and Euler-Bernoulli equations.- New results in shape optimization.- Shape formulation of free boundary problems with non linearized Bernoulli condition.
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Elsevier eBooks, 1990
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Control and Cybernetics, 2009
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Comptes rendus de l'Académie des sciences, 1997
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Applied Mathematics and Optimization, 1997
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Georgian Mathematical Journal
Non-smooth evolution in thermo-viscoplastic flows is investigated. The nonlinear Norton–Hoff mode... more Non-smooth evolution in thermo-viscoplastic flows is investigated. The nonlinear Norton–Hoff model coupled with the unsteady heat system govern the fluid motion. This contribution is an extension of the previous established works. The novelty of this paper is to supply a close scrutiny result of the spawned interface through the medium of the pervasive Schauder fixed point. Numerical results are exhibited to illustrate the effectiveness of the advocated approach.
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We consider a shape formulation of free boundary problem arising from plasmas physics. That probl... more We consider a shape formulation of free boundary problem arising from plasmas physics. That problem has a non differentiable variational formulation in the variable y ∈ 0 1 (Γ D ). By a change of variable we rewrite this variational formulation as a shape optimization problem for some shape cost functional J(Γ) in the form Min {J in (Γ,u) / u ∈H 1 (Γ)} + Min { J out (Γ C ,v) / v ∈H 0 1 (Γ C )}. The change of variable is of the form y = uX Γ + (1 - X Γ )v and J turns to be smooth with respect to Γ and we compute the two first shape derivatives (see (12)). In fact Γ is a subset of a smooth surface and we shall do shape calculus using intrinsic geometrical approach with generalized Laplace Beltrami operators.
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Shapes and Geometries, 2011
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Conference Publications 2011, 2011
ABSTRACT A linearized steady state three-dimensional fluid-structure interac-tion is considered a... more ABSTRACT A linearized steady state three-dimensional fluid-structure interac-tion is considered and its solvability is studied. The linearization (obtained in a previous work by these authors) that we deal with has new features, including the presence of the curvature terms on the common interface. These new extra terms, coming from the geometrical aspect of the problem, are critical for a correct physical interpretation of the fluid/structure coupling. We prove that the linearization has unique solution.
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Nonlinear Analysis: Real World Applications, 2018
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Acoustics, Mechanics, and the Related Topics of Mathematical Analysis, 2003
The controlled evolution of level sets provides a successful framework to solve time-harmonic inv... more The controlled evolution of level sets provides a successful framework to solve time-harmonic inverse scattering problems for objects whose contrast with the environment is known but whose shape is unknown. New solution tools extend this framework to the retrieval of objects whose both shape and contrast are unknown
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Journal of Differential Equations, Dec 1, 2015
Bookmarks Related papers MentionsView impact
Computer Methods in Applied Mechanics and Engineering, Aug 1, 1985
Bookmarks Related papers MentionsView impact
IFAC Proceedings Volumes, Jul 1, 1984
Bookmarks Related papers MentionsView impact
Springer eBooks, Sep 19, 2008
In this paper, we use the concept of connecting tubes introduced in [7][5] and we consider the ge... more In this paper, we use the concept of connecting tubes introduced in [7][5] and we consider the geodesic tube construction between two sets according to the tube shape metric. The first section is devoted to the tube analysis and formulation associated to the Galerkin-Level Set strategy. This new variational formulation consists in parameterizing the level set function in a finite vector space. Consequently, the aim of a Galerkin-Level Set method is more focused on topology that on high accuracy for the boundary approximation. However, the main advantage of this method, over the traditional level set formulation, concerns the standard partial differential equation (PDE) evolution for the level set function that, in the Galerkin-Level Set method turns into a system of ordinary differential equations and we avoid any “usual” instability. The second section concerns a shape identification problem associated to an Hilbert space metric using the Galerkin-Level Set method. In the last section, the geodesic tube construction is made by a optimization process based on a shape gradient calculus. Finally, a geodesic tube construction between two sets is validated by numerical experiments in 3D.
Bookmarks Related papers MentionsView impact
Inverse Problems, 1999
ABSTRACT We are interested in a dynamical shape control problem in hydrodynamics. The considered ... more ABSTRACT We are interested in a dynamical shape control problem in hydrodynamics. The considered cost functional is the kinetic energy of a perfect and incompressible fluid. We establish the existence of a non-autonomous vector field which constructs the tube followed by the fluid in such a way as to minimize its kinetic energy. By introducing a specific adjoint state closely related to the shape of the tube, we derive the necessary optimality condition.
Bookmarks Related papers MentionsView impact
Journal of Functional Analysis, Feb 1, 1992
Bookmarks Related papers MentionsView impact
Siam Journal on Control and Optimization, Jul 1, 1988
Bookmarks Related papers MentionsView impact
Springer eBooks, 1990
Recent work on the scole model.- Mathematical study of large space structures.- Symbolic formulat... more Recent work on the scole model.- Mathematical study of large space structures.- Symbolic formulation of dynamic equations for interconnected flexible bodies: The GEMMES software.- Adaptive optics - Shape control of an adaptive mirror.- Energy decay estimates for a beam with nonlinear boundary feedback.- Uniform stabilization of the wave equation with dirichlet-feedback control without geometrical conditions.- Actuators and controllability of distributed systems.- Linear quadratic control problem without stabilizability.- Riccati equations in noncylindrical domains.- Boundary control problems for non-autonomous parabolic systems.- Existence and optimal control for wave equation in moving domain.- Galerkine approximation for wave equation in moving domain.- Further results on exact controllability of the Euler-Bernoulli equation with controls on the dirichlet and neumann boundary conditions.- Some properties of the value function of a nonlinear control problem in infinite dimensions.- Identification of coefficients with bounded variation in the wave equation.- Shape hessian by the velocity method: A Lagrangian approach.- Shape sensitivity analysis of hyperbolic problems.- Differential stability of perturbed optimization with applications to parameter estimation.- A numerical method for drag minimization via the suction and injection of mass through the boundary.- Using the physical properties of systems for control: An illustration.
Bookmarks Related papers MentionsView impact
Control of an overhead crane: Stabilization of flexibilities.- Exact controllability for linear d... more Control of an overhead crane: Stabilization of flexibilities.- Exact controllability for linear dynamic systems with skew symmetric operators.- Boundary homogenization and boundary shape optimization for a cylinder.- Relaxed formulation for a class of shape optimization problems.- On the smoothness of the value function along optimal trajectories.- Some boundary control problems and computation for the linear elastostatic kirchhoff plate on an exterior domain.- Approximate controllability for the wave equation.- Truss structures: Fourier conditions and eigenvalue problem.- Boundary control and stabilization of the one-dimensional wave equation.- Boundary control for inverse free boundary problems.- Differentiability of Min Max and saddle points under relaxed assumptions.- New noniterative approximations to the old riccati differential equation.- Numerical approach to the exact controllability of hyperbolic systems.- Shape sensitivity analysis for stochastic evolution equations.- Boundary controllability problems for the wave and heat equations.- About critical points of the energy in an electromagnetic shaping problem.- Finite dimesional compensator for flexible structures.- Remarks on boundary control for polyhedral domains and related results.- Stability of the travelling waves in a class of free boundary problems arising in combustion theory.- A convergent finite element scheme for a wave equation with a moving boundary.- A boundary controllability approach in optimal shape design problems.- Regularity with interior point control. Part I: Wave and Euler-Bernoulli equations.- New results in shape optimization.- Shape formulation of free boundary problems with non linearized Bernoulli condition.
Bookmarks Related papers MentionsView impact
Elsevier eBooks, 1990
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Control and Cybernetics, 2009
Bookmarks Related papers MentionsView impact
Comptes rendus de l'Académie des sciences, 1997
Bookmarks Related papers MentionsView impact
Applied Mathematics and Optimization, 1997
Bookmarks Related papers MentionsView impact
Georgian Mathematical Journal
Non-smooth evolution in thermo-viscoplastic flows is investigated. The nonlinear Norton–Hoff mode... more Non-smooth evolution in thermo-viscoplastic flows is investigated. The nonlinear Norton–Hoff model coupled with the unsteady heat system govern the fluid motion. This contribution is an extension of the previous established works. The novelty of this paper is to supply a close scrutiny result of the spawned interface through the medium of the pervasive Schauder fixed point. Numerical results are exhibited to illustrate the effectiveness of the advocated approach.
Bookmarks Related papers MentionsView impact
We consider a shape formulation of free boundary problem arising from plasmas physics. That probl... more We consider a shape formulation of free boundary problem arising from plasmas physics. That problem has a non differentiable variational formulation in the variable y ∈ 0 1 (Γ D ). By a change of variable we rewrite this variational formulation as a shape optimization problem for some shape cost functional J(Γ) in the form Min {J in (Γ,u) / u ∈H 1 (Γ)} + Min { J out (Γ C ,v) / v ∈H 0 1 (Γ C )}. The change of variable is of the form y = uX Γ + (1 - X Γ )v and J turns to be smooth with respect to Γ and we compute the two first shape derivatives (see (12)). In fact Γ is a subset of a smooth surface and we shall do shape calculus using intrinsic geometrical approach with generalized Laplace Beltrami operators.
Bookmarks Related papers MentionsView impact
Shapes and Geometries, 2011
Bookmarks Related papers MentionsView impact
Conference Publications 2011, 2011
ABSTRACT A linearized steady state three-dimensional fluid-structure interac-tion is considered a... more ABSTRACT A linearized steady state three-dimensional fluid-structure interac-tion is considered and its solvability is studied. The linearization (obtained in a previous work by these authors) that we deal with has new features, including the presence of the curvature terms on the common interface. These new extra terms, coming from the geometrical aspect of the problem, are critical for a correct physical interpretation of the fluid/structure coupling. We prove that the linearization has unique solution.
Bookmarks Related papers MentionsView impact
Nonlinear Analysis: Real World Applications, 2018
Bookmarks Related papers MentionsView impact
Acoustics, Mechanics, and the Related Topics of Mathematical Analysis, 2003
The controlled evolution of level sets provides a successful framework to solve time-harmonic inv... more The controlled evolution of level sets provides a successful framework to solve time-harmonic inverse scattering problems for objects whose contrast with the environment is known but whose shape is unknown. New solution tools extend this framework to the retrieval of objects whose both shape and contrast are unknown
Bookmarks Related papers MentionsView impact