## IKEHATA Ryo, SOBUKAWA Genta,

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

## Hokkaido Mathematical Journal, 36 (2007) pp.53-71

### Fulltext

PDF### 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.

MSC(Primary) | 35L05 |
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MSC(Secondary) | 35B40 |

Uncontrolled Keywords | hyperbolic equation, exterior mixed problem, weighted initial data, local energy decay |