Displaying similar documents to “On the Stabilization of the Wave Equation by the Boundary”

On the Uniform Decay of the Local Energy

Vodev, Georgi (1999)

Serdica Mathematical Journal

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It is proved in [1],[2] that in odd dimensional spaces any uniform decay of the local energy implies that it must decay exponentially. We extend this to even dimensional spaces and to more general perturbations (including the transmission problem) showing that any uniform decay of the local energy implies that it must decay like O(t^(−2n) ), t ≫ 1 being the time and n being the space dimension.

Decay of solutions of the wave equation in the exterior of several convex bodies

Mitsuru Ikawa (1988)

Annales de l'institut Fourier

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We study the decay of solutions to the wave equation in the exterior of several strictly convex bodies. A sufficient condition for exponential decay of the local energy is expressed in terms of the period and the Poincare map of periodic rays in the exterior domain.

Asymptotic stability of wave equations with memory and frictional boundary dampings

Fatiha Alabau-Boussouira (2008)

Applicationes Mathematicae

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This work is concerned with stabilization of a wave equation by a linear boundary term combining frictional and memory damping on part of the boundary. We prove that the energy decays to zero exponentially if the kernel decays exponentially at infinity. We consider a slightly different boundary condition than the one used by M. Aassila et al. [Calc. Var. 15, 2002]. This allows us to avoid the assumption that the part of the boundary where the feedback is active is strictly star-shaped....