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Research paper thumbnail of A pseudo-extractor approach to hidden boundary regularity for the wave equation with mixed boundary conditions

Journal of Differential Equations, Dec 1, 2015

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Research paper thumbnail of An optimal triangulation for second-order elliptic problems

Computer Methods in Applied Mechanics and Engineering, Aug 1, 1985

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Research paper thumbnail of Optimal Location of a Control in a Parabolic Equation

IFAC Proceedings Volumes, Jul 1, 1984

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Research paper thumbnail of Moving Domain by Galerkin-Level Set Strategy: Application to Shape Geodesics

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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Research paper thumbnail of Dynamical shape control in non-cylindrical hydrodynamics

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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Research paper thumbnail of Structure of shape derivatives for nonsmooth domains

Journal of Functional Analysis, Feb 1, 1992

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Research paper thumbnail of Shape Sensitivity Analysis via Min Max Differentiability

Siam Journal on Control and Optimization, Jul 1, 1988

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Research paper thumbnail of Stabilization of flexible structures : third working conference Montpellier, France, January 1989

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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Research paper thumbnail of Boundary control and boundary variation : proceedings of IFIP WG 7.2 Conference, Sophia Antipolis, France, October 15-17, 1990

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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Research paper thumbnail of Stabilization of Wave Equation by Periodical Moving Actuators

Elsevier eBooks, 1990

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Research paper thumbnail of Shape-Morphing Metric by Variational Formulation for In- compressible Euler Flow

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Research paper thumbnail of Variational formulation for incompressible Euler flow/ shape-morphing metric and geodesic

Control and Cybernetics, 2009

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Research paper thumbnail of Stabilité du spectre d'un opérateur elliptique par rapport au domaine

Comptes rendus de l'Académie des sciences, 1997

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Research paper thumbnail of Shape-sensitivity analysis for nonlinear heat convection

Applied Mathematics and Optimization, 1997

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Research paper thumbnail of Non-smooth evolution of non-Newtonian flows influenced by thermal effects

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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Research paper thumbnail of Shape Hessian for a Nondifferentiable Variational Free Boundary Problem

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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Research paper thumbnail of 3. Courant Metrics on Images of a Set

Shapes and Geometries, 2011

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Research paper thumbnail of Existence for the linearization of a steady state fluid/nonlinear elasticity interaction

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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Research paper thumbnail of Stabilization of wave dynamics by moving boundary

Nonlinear Analysis: Real World Applications, 2018

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Research paper thumbnail of On the Controlled Evolution of Level Sets and Like Methods: The Shape and Contrast Reconstruction

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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Research paper thumbnail of A pseudo-extractor approach to hidden boundary regularity for the wave equation with mixed boundary conditions

Journal of Differential Equations, Dec 1, 2015

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Research paper thumbnail of An optimal triangulation for second-order elliptic problems

Computer Methods in Applied Mechanics and Engineering, Aug 1, 1985

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Research paper thumbnail of Optimal Location of a Control in a Parabolic Equation

IFAC Proceedings Volumes, Jul 1, 1984

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Research paper thumbnail of Moving Domain by Galerkin-Level Set Strategy: Application to Shape Geodesics

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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Research paper thumbnail of Dynamical shape control in non-cylindrical hydrodynamics

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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Research paper thumbnail of Structure of shape derivatives for nonsmooth domains

Journal of Functional Analysis, Feb 1, 1992

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Research paper thumbnail of Shape Sensitivity Analysis via Min Max Differentiability

Siam Journal on Control and Optimization, Jul 1, 1988

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Stabilization of flexible structures : third working conference Montpellier, France, January 1989

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

Research paper thumbnail of Boundary control and boundary variation : proceedings of IFIP WG 7.2 Conference, Sophia Antipolis, France, October 15-17, 1990

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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Research paper thumbnail of Stabilization of Wave Equation by Periodical Moving Actuators

Elsevier eBooks, 1990

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Research paper thumbnail of Shape-Morphing Metric by Variational Formulation for In- compressible Euler Flow

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Variational formulation for incompressible Euler flow/ shape-morphing metric and geodesic

Control and Cybernetics, 2009

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Research paper thumbnail of Stabilité du spectre d'un opérateur elliptique par rapport au domaine

Comptes rendus de l'Académie des sciences, 1997

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Research paper thumbnail of Shape-sensitivity analysis for nonlinear heat convection

Applied Mathematics and Optimization, 1997

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Research paper thumbnail of Non-smooth evolution of non-Newtonian flows influenced by thermal effects

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

Research paper thumbnail of Shape Hessian for a Nondifferentiable Variational Free Boundary Problem

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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Research paper thumbnail of 3. Courant Metrics on Images of a Set

Shapes and Geometries, 2011

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Research paper thumbnail of Existence for the linearization of a steady state fluid/nonlinear elasticity interaction

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

Research paper thumbnail of Stabilization of wave dynamics by moving boundary

Nonlinear Analysis: Real World Applications, 2018

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Research paper thumbnail of On the Controlled Evolution of Level Sets and Like Methods: The Shape and Contrast Reconstruction

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