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Energy decay for the wave equation with boundary and localized dissipations in exterior domains

✍ Scribed by Jeong Ja Bae; Mitsuhiro Nakao

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 186 KB
Volume: 278
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200310271

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✦ Synopsis

Abstract

We study a decay property of solutions for the wave equation with a localized dissipation and a boundary dissipation in an exterior domain Ω with the boundary ∂Ω = Γ~0~ ∪ Γ~1~, Γ~0~ ∩ Γ~1~ = ∅︁. We impose the homogeneous Dirichlet condition on Γ~0~ and a dissipative Neumann condition on Γ~1~. Further, we assume that a localized dissipation a(x)u~t~ is effective near infinity and in a neighborhood of a certain part of the boundary Γ~0~. Under these assumptions we derive an energy decay like E(t) ≤ C(1 + t)^–1^ and some related estimates. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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