Pointwise controllability as limit of internal controllability for the wave equation in one space dimension.
Inégalités de Carleman globales pour les problèmes elliptiques non homogènes
On établit ici, suivant [5], une inégalité de Carleman globale optimale pour les solutions faibles (au sens ) d’équations elliptiques générales avec second membre dans et trace non nulle. La motivation, qui est expliquée dans l’introduction, réside dans l’obtention d’inégalités de Carleman globale pour l’opérateur de Navier-Stokes linéarisé afin, notamment, d’étudier les questions de contrôlabilité exacte sur les trajectoires pour les équations de Navier-Stokes. Une étape majeure...
Approximate controllability for a linear model of fluid structure interaction
Unique continuation property near a corner and its fluid-structure controllability consequences
We study a non standard unique continuation property for the biharmonic spectral problem in a 2D corner with homogeneous Dirichlet boundary conditions and a supplementary third order boundary condition on one side of the corner. We prove that if the corner has an angle , and , a unique continuation property holds. Approximate controllability of a 2-D linear fluid-structure problem follows from this property, with a control acting on the elastic side of a corner in a domain containing a Stokes...
Approximate controllability for a system of Schrödinger equations modeling a single trapped ion
Boundary sentinels with given sensitivity.
Approximate controllability for a linear model of fluid structure interaction
We consider a linear model of interaction between a viscous incompressible fluid and a thin elastic structure located on a part of the fluid domain boundary, the other part being rigid. After having given an existence and uniqueness result for the direct problem, we study the question of approximate controllability for this system when the control acts as a normal force applied to the structure. The case of an analytic boundary has been studied by Lions and Zuazua in [9] where, in particular,...
Unique continuation property near a corner and its fluid-structure controllability consequences
We study a non standard unique continuation property for the biharmonic spectral problem in a 2D corner with homogeneous Dirichlet boundary conditions and a supplementary third order boundary condition on one side of the corner. We prove that if the corner has an angle , and , a unique continuation property holds. Approximate controllability of a 2-D linear fluid-structure problem follows from this property, with a control acting on the elastic side of a corner in a domain containing...
A null controllability data assimilation methodology applied to a large scale ocean circulation model
Data assimilation refers to any methodology that uses partial observational data and the dynamics of a system for estimating the model state or its parameters. We consider here a non classical approach to data assimilation based in null controllability introduced in [Puel, 335 (2002) 161–166] and [Puel, 48 (2009) 1089–1111] and we apply it to oceanography. More precisely, we are interested in developing this methodology to recover the unknown final state value (state value at the end of the measurement...
Flambage des plaques élastiques multiperforées
A null controllability data assimilation methodology applied to a large scale ocean circulation model
Data assimilation refers to any methodology that uses partial observational data and the dynamics of a system for estimating the model state or its parameters. We consider here a non classical approach to data assimilation based in null controllability introduced in [Puel, (2002) 161–166] and [Puel, (2009) 1089–1111] and we apply it to oceanography. More precisely, we are interested in developing this methodology to recover the unknown final state value (state...
Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case
This paper is concerned with the global exact controllability of the semilinear heat equation (with nonlinear terms involving the state and the gradient) completed with boundary conditions of the form . We consider distributed controls, with support in a small set. The null controllability of similar linear systems has been analyzed in a previous first part of this work. In this second part we show that, when the nonlinear terms are locally Lipschitz-continuous and slightly superlinear, one...
Null controllability of the heat equation with boundary Fourier conditions: the linear case
In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form . We consider distributed controls with support in a small set and nonregular coefficients . For the proof of null controllability, a crucial tool will be a new Carleman estimate for the weak solutions of the classical heat equation with nonhomogeneous Neumann boundary conditions.
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