Issue |
ESAIM: Proc.
Volume 8, 2000
Contrôle des systèmes gouvernés par des équations aux dérivées partielles
|
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Page(s) | 119 - 136 | |
DOI | https://doi.org/10.1051/proc:2000009 | |
Published online | 15 August 2002 |
Stabilization for the wave equation with Neumann boundary condition by a locally distributed damping
Département de Mathématiques, E. N. S. Cachan, Antenne de Bretagne, Campus de Ker Lann, 35170 Bruz, France
We consider the problem of the wave equation with Neumann boundary condition damped by a locally distributed linear damping a(x)u'. When the damping region ω : = {x, a(x) ≥ a > 0} contains a neighborhood of the boundary of the domain, E. Zuazua proved that the energy decays exponentially to zero. Using a piecewise multiplier method introduced by K. Liu, we prove that the energy decays exponentially to zero under weaker geometrical conditions. We give explicit examples when the domain is a polyhedron, and in the case of a disc. The proof is based on the construction of multipliers adapted to the geometrical conditions.
© EDP Sciences, ESAIM, 2000
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