### Abstract

We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition and study the asymptotic behavior of the solution for large times. For possible application we are interested to show a decay estimate which does not involve weighted norms of the initial data. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.

Original language | English |
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Pages (from-to) | 221-236 |

Number of pages | 16 |

Journal | Journal of Differential Equations |

Volume | 194 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2003 Oct 10 |

### Fingerprint

### Keywords

- Asymptotic behavior
- Decay rate
- Exterior domain
- Local energy decay
- Neumann boundary condition
- Wave equation

### ASJC Scopus subject areas

- Analysis

### Cite this

**On the decay of solutions to the 2D Neumann exterior problem for the wave equation.** / Secchi, Paolo; Shibata, Yoshihiro.

Research output: Contribution to journal › Article

*Journal of Differential Equations*, vol. 194, no. 1, pp. 221-236. https://doi.org/10.1016/S0022-0396(03)00189-X

}

TY - JOUR

T1 - On the decay of solutions to the 2D Neumann exterior problem for the wave equation

AU - Secchi, Paolo

AU - Shibata, Yoshihiro

PY - 2003/10/10

Y1 - 2003/10/10

N2 - We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition and study the asymptotic behavior of the solution for large times. For possible application we are interested to show a decay estimate which does not involve weighted norms of the initial data. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.

AB - We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition and study the asymptotic behavior of the solution for large times. For possible application we are interested to show a decay estimate which does not involve weighted norms of the initial data. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.

KW - Asymptotic behavior

KW - Decay rate

KW - Exterior domain

KW - Local energy decay

KW - Neumann boundary condition

KW - Wave equation

UR - http://www.scopus.com/inward/record.url?scp=0141615003&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141615003&partnerID=8YFLogxK

U2 - 10.1016/S0022-0396(03)00189-X

DO - 10.1016/S0022-0396(03)00189-X

M3 - Article

VL - 194

SP - 221

EP - 236

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 1

ER -