### 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} = Ø. 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.

Original language | English |
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Pages (from-to) | 771-783 |

Number of pages | 13 |

Journal | Mathematische Nachrichten |

Volume | 278 |

Issue number | 7-8 |

DOIs | |

Publication status | Published - 2005 |

Externally published | Yes |

### Fingerprint

### Keywords

- Dissipation
- Energy decay
- Exterior problem
- Wave equation

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematische Nachrichten*,

*278*(7-8), 771-783. https://doi.org/10.1002/mana.200310271

**Energy decay for the wave equation with boundary and localized dissipations in exterior domains.** / Bae, Jeong Ja; Nakao, Mitsuhiro.

Research output: Contribution to journal › Article

*Mathematische Nachrichten*, vol. 278, no. 7-8, pp. 771-783. https://doi.org/10.1002/mana.200310271

}

TY - JOUR

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

UR - http://www.scopus.com/inward/record.url?scp=20444369234&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=20444369234&partnerID=8YFLogxK

U2 - 10.1002/mana.200310271

DO - 10.1002/mana.200310271

M3 - Article

AN - SCOPUS:20444369234

VL - 278

SP - 771

EP - 783

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

IS - 7-8

ER -