## Abstract We study a decay property of solutions for the wave equation with a localized dissipation and a boundary dissipation in an exterior domain Ξ© with the boundary βΞ© = Ξ~0~ βͺ Ξ~1~, Ξ~0~ β© Ξ~1~ = β οΈ. We impose the homogeneous Dirichlet condition on Ξ~0~ and a dissipative Neumann condition on
Energy decay for the linear and semilinear wave equations in exterior domains with some localized dissipations
β Scribed by Mitsuhiro Nakao
- Publisher
- Springer-Verlag
- Year
- 2001
- Tongue
- French
- Weight
- 146 KB
- Volume
- 238
- Category
- Article
- ISSN
- 0025-5874
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π SIMILAR VOLUMES
## Abstract We shall derive some global existence results to semilinear wave equations with a damping coefficient localized near infinity for very special initial data in __H__Γ__L__^2^. This problem is dealt with in the twoβdimensional exterior domain with a starβshaped complement. In our result,
We derive a fast decay estimate for the wave equation with a local degenerate dissipation of the type a(x)u t in a bounded domain β¦. The dissipative coefficient a(x) is a nonnegative function only on a neighborhood of some part of the boundary ββ¦ and may vanish somewhere in β¦. The results obtained e