Stabilization of local energy in an exterior domain for the wave equation with a localized dissipation

Mitsuhiro Nakao

doi:10.1006/jdeq.1998.3468

Stabilization of local energy in an exterior domain for the wave equation with a localized dissipation

Mitsuhiro Nakao^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

32 Citations (Scopus)

Abstract

We derive an algebraic decay rate for the local energy E_loc(t) of the solutions to the initial-boundary value problem of the wave equation with a localized dissipation in an exterior domain Ω. The dissipative term a(x) u_t is assumed to be effective only on a neighbourhood of a part of the boundary Γ(x₀) = {x∈∂Ω

Original language	English
Pages (from-to)	388-406
Number of pages	19
Journal	Journal of Differential Equations
Volume	148
Issue number	2
DOIs	https://doi.org/10.1006/jdeq.1998.3468
Publication status	Published - 1998
Externally published	Yes

ASJC Scopus subject areas

Analysis

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10.1006/jdeq.1998.3468

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abstract = "We derive an algebraic decay rate for the local energy Eloc(t) of the solutions to the initial-boundary value problem of the wave equation with a localized dissipation in an exterior domain Ω. The dissipative term a(x) ut is assumed to be effective only on a neighbourhood of a part of the boundary Γ(x0) = {x∈∂Ω",

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Stabilization of local energy in an exterior domain for the wave equation with a localized dissipation

Abstract

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