## Hokkaido Mathematical Journal

- Hokkaido Math. J.
- Volume 36, Number 1 (2007), 53-71.

### Local energy decay for some hyperbolic equations with initial data decaying slowly near infinity

Ryo IKEHATA and Genta SOBUKAWA

#### Abstract

A uniform local energy decay property is discussed to a linear hyperbolic equation with spatial variable coefficients. We shall deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we assume algebraic order weight restrictions as $\vert x\vert \to +\infty$ on the initial data in order to derive the uniform local energy decay, and its proof is quite simple.

#### Article information

**Source**

Hokkaido Math. J., Volume 36, Number 1 (2007), 53-71.

**Dates**

First available in Project Euclid: 29 September 2010

**Permanent link to this document**

https://projecteuclid.org/euclid.hokmj/1285766662

**Digital Object Identifier**

doi:10.14492/hokmj/1285766662

**Mathematical Reviews number (MathSciNet)**

MR2309821

**Zentralblatt MATH identifier**

1135.35018

**Subjects**

Primary: 35L05: Wave equation

Secondary: 35B40: Asymptotic behavior of solutions

**Keywords**

hyperbolic equation exterior mixed problem weighted initial data local energy decay

#### Citation

IKEHATA, Ryo; SOBUKAWA, Genta. Local energy decay for some hyperbolic equations with initial data decaying slowly near infinity. Hokkaido Math. J. 36 (2007), no. 1, 53--71. doi:10.14492/hokmj/1285766662. https://projecteuclid.org/euclid.hokmj/1285766662