Hokkaido Mathematical Journal

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

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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
MSC(Secondary)35B40
Uncontrolled Keywordshyperbolic equation, exterior mixed problem, weighted initial data, local energy decay