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Contrôlabilité exacte d'un problème avec conditions de Ventcel évolutives pour le système linéaire de l'élasticité.

Amar Heminna — 2001

Revista Matemática Complutense

In this work, we examine the exact controllability of the solution of a linear elasticity system, with evolutive Ventcel's conditions, (see [3]), in a bounded domain of R. We use the Hilbert uniqueness methode, (H.U.M), of J.L.Lions, (see [9]); some multipliers are defined on the boundary; the curvature tensor (see [6]), appears when computing some boundary integrals. This work can be inserted in the framework of the study of the exact controllability and stabilisation of various problems with Ventcel's...

Stabilisation frontière de problèmes de Ventcel

Amar Heminna — 2010

ESAIM: Control, Optimisation and Calculus of Variations

The problem of boundary stabilization for the isotropic linear elastodynamic system and the wave equation with Ventcel's conditions are considered (see [12]). The boundary observability and the exact controllability were etablished in [11]. We prove here the enegy decay to zero for the elastodynamic system with stationary Ventcel's conditions by introducing a nonlinear boundary feedback. We also give a boundary feedback leading to arbitrarily large energy decay rates for the elastodynamic system...

Boundary stabilization of the linear elastodinamic system by a Lyapunov-type method.

Rabah BeyAmar HeminnaJean-Pierre Lohéac — 2003

Revista Matemática Complutense

We propose a direct approach to obtain the boundary stabilization of the isotropic linear elastodynamic system by a natural feedback; this method uses local coordinates in the expression of boundary integrals as a main tool. It leads to an explicit decay rate of the energy function and requires weak geometrical conditions: for example, the spacial domain can be the difference of two star-shaped sets.

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