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Local energy decay for a class of hyperbolic equations with constant coefficients near infinity

✍ Scribed by Shintaro Aikawa; Ryo Ikehata

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 162 KB
Volume: 283
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200710009

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✦ Synopsis

Hyperbolic equations, exterior mixed problems, non-compactly supported initial data, local energy decay MSC (2000) 35L05; 35B40

A uniform local energy decay result is derived to a compactly perturbed hyperbolic equation with spatial variable coefficients. We shall deal with this equation in an N -dimensional exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data and the equation includes anisotropic variable coefficients {ai(x) : i = 1, 2, . . . , N}, which are not necessarily equal to each other.

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