Geodesic
Stabilization for the wave equation with Neumann boundary condition by a locally distributed damping
Patrick Martinez1
1 Département de Mathématiques, E. N. S. Cachan, Antenne de Bretagne, Campus de Ker Lann, 35170 Bruz, France
ESAIM. Proceedings, Tome 8 (2000), pp. 119-136 Cet article a éte moissonné depuis la source EDP Sciences

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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.
DOI : 10.1051/proc:2000009

Patrick Martinez 1

1 Département de Mathématiques, E. N. S. Cachan, Antenne de Bretagne, Campus de Ker Lann, 35170 Bruz, France 
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     author = {Patrick Martinez},
     title = {Stabilization for the wave equation with {Neumann} boundary condition by a locally distributed damping},
     journal = {ESAIM. Proceedings},
     pages = {119--136},
     year = {2000},
     volume = {8},
     doi = {10.1051/proc:2000009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:2000009/}
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Patrick Martinez. Stabilization for the wave equation with Neumann boundary condition by a locally distributed damping. ESAIM. Proceedings, Tome 8 (2000), pp. 119-136. doi: 10.1051/proc:2000009

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