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- W2550242794 abstract "We consider a damped wave equation on a open subset of Rn or a smooth Riemannian manifold with boundary, with Ventcel boundary conditions, with a linear damping, acting either in the interior or at the boundary. This equation is a model for a vibrating structure with a layer with higher rigidity of thickness δ>0. By means of a proper Carleman estimate for second-order elliptic operators near the boundary, we derive a resolvent estimate for the wave semigroup generator along the imaginary axis, which in turn yields the logarithmic decay rate of the energy. This stabilization result is obtained uniformly in δ. On considère l'équation des ondes amorties sur un ouvert régulier borné de Rn, ou sur une variété riemannienne à bord, avec conditions de Ventcel, avec un amortissement linéaire, agissant soit à l'intérieur, soit au bord. Cette équation avec ces conditions au bord modélisent les vibrations d'une structure avec une couche fine d'épaisseur δ>0, de plus grande rigidité. Avec une inégalité de Carleman locale au voisinage du bord adaptée, on montre une inégalité de résolvante pour le générateur du semi-groupe des ondes le long de l'axe imaginaire, qui implique une décroissance logarithmique de l'énergie uniforme en le paramètre δ." @default.
- W2550242794 created "2016-11-30" @default.
- W2550242794 creator A5036125701 @default.
- W2550242794 date "2017-08-01" @default.
- W2550242794 modified "2023-10-14" @default.
- W2550242794 title "Stabilization of the wave equation with Ventcel boundary condition" @default.
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- W2550242794 doi "https://doi.org/10.1016/j.matpur.2016.11.001" @default.
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