Exact controllability of vibrations of thin bodies.
Sur une méthode d'éléments finis mixte pour l'équation biharmonique
Fourier approach to homogenization problems
This article is divided into two chapters. The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in the first chapter. Following a Fourier approach, we discuss some of the basic issues of the subject: main convergence theorem, Bloch approximation, estimates on second order derivatives, correctors for the medium, and so on. The second chapter is devoted to the discussion of some non-classical behaviour of vibration problems of periodic...
Controllability of a simplified model of fluid-structure interaction
This article aims at studying the controllability of a simplified fluid structure interaction model derived and developed in [C. Conca, J. Planchard and M. Vanninathan, John Wiley & Sons Ltd., Chichester (1995); J.-P. Raymond and M. Vanninathan, 11 (2005) 180–203; M. Tucsnak and M. Vanninathan, 58 (2009) 547–552]. This interaction is modeled by a wave equation surrounding a harmonic oscillator. Our main result states that, in the radially symmetric case, this system can be controlled from the...
Fourier approach to homogenization problems
This article is divided into two chapters. The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in the first chapter. Following a Fourier approach, we discuss some of the basic issues of the subject: main convergence theorem, Bloch approximation, estimates on second order derivatives, correctors for the medium, and so on. The second chapter is devoted to the discussion of some non-classical behaviour of vibration problems of periodic...
On the regularity of the variational solution of the Tricomi problem in the elliptic region
Vibrations of thin elastic structures and exact controllability
Approximation of Tricomi Problem with Neumann Boundary Condition.
Boundary sentinels in cylindrical domains.
We study a model describing vibrations of a cylindrical domain with thickness e > 0. A characteristic of this model is that it contains pollution terms in the boundary data and missing terms in the initial data. The method of sentinels'' of J. L. Lions [7] is followed to construct a sentinel using the observed vibrations on the boundary. Such a sentinel, by construction, provides information on pollution terms independent of missing terms. This requires resolution of initial-boundary value...
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