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Lp-estimates for the wave equation with time-dependent dissipation

Published online by Cambridge University Press:  12 July 2007

Tokio Matsuyama
Tokio Matsuyama
Affiliation:
Department of Mathematics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan (matsu@sm.u-tokai.ac.jp)
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Abstract

We are interested in Lp-estimates and scattering rates for the dissipative wave equation with time-dependent coefficients in an exterior domain outside a star-shaped obstacle. We want to notice the case that the support of dissipation expands strictly less than the wave speed. We develop a new cut-off method, which is time dependent. For this, we shall obtain the local energy decay over the time-dependent subdomain

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 2 , April 2005 , pp. 393 - 412
Copyright
Copyright © Royal Society of Edinburgh 2005

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