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

Jeong Ja Bae; Mitsuhiro Nakao

doi:10.1002/mana.200310271

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

Jeong Ja Bae, Mitsuhiro Nakao^*

^*Corresponding author for this work

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

14 Citations (Scopus)

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, = Γ₀ ∪ Γ₁, Γ₀ ∩ Γ₁ = Ø. We impose the homogeneous Dirichlet condition on Γ₀ and a dissipative Neumann condition on Γ₁. 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 Γ₀. Under these assumptions we derive an energy decay like E(t) ≤ C(1 + t)^-1 and some related estimates.

Original language	English
Pages (from-to)	771-783
Number of pages	13
Journal	Mathematische Nachrichten
Volume	278
Issue number	7-8
DOIs	https://doi.org/10.1002/mana.200310271
Publication status	Published - 2005
Externally published	Yes

Keywords

Dissipation
Energy decay
Exterior problem
Wave equation

ASJC Scopus subject areas

Mathematics(all)

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10.1002/mana.200310271

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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, = Γ0 ∪ Γ1, Γ0 ∩ Γ1 = {\O}. We impose the homogeneous Dirichlet condition on Γ0 and a dissipative Neumann condition on Γ1. Further, we assume that a localized dissipation a(x)ut is effective near infinity and in a neighborhood of a certain part of the boundary Γ0. Under these assumptions we derive an energy decay like E(t) ≤ C(1 + t)-1 and some related estimates.",

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author = "Bae, {Jeong Ja} and Mitsuhiro Nakao",

year = "2005",

doi = "10.1002/mana.200310271",

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journal = "Mathematische Nachrichten",

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T1 - Energy decay for the wave equation with boundary and localized dissipations in exterior domains

AU - Bae, Jeong Ja

AU - Nakao, Mitsuhiro

PY - 2005

Y1 - 2005

N2 - 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, = Γ0 ∪ Γ1, Γ0 ∩ Γ1 = Ø. We impose the homogeneous Dirichlet condition on Γ0 and a dissipative Neumann condition on Γ1. Further, we assume that a localized dissipation a(x)ut is effective near infinity and in a neighborhood of a certain part of the boundary Γ0. Under these assumptions we derive an energy decay like E(t) ≤ C(1 + t)-1 and some related estimates.

AB - 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, = Γ0 ∪ Γ1, Γ0 ∩ Γ1 = Ø. We impose the homogeneous Dirichlet condition on Γ0 and a dissipative Neumann condition on Γ1. Further, we assume that a localized dissipation a(x)ut is effective near infinity and in a neighborhood of a certain part of the boundary Γ0. Under these assumptions we derive an energy decay like E(t) ≤ C(1 + t)-1 and some related estimates.

KW - Dissipation

KW - Energy decay

KW - Exterior problem

KW - Wave equation

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DO - 10.1002/mana.200310271

M3 - Article

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SN - 0025-584X

VL - 278

SP - 771

EP - 783

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 7-8

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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