### Energy decay for a nonlinear generalized Klein-Gordon equation in exterior domains with a nonlinear localized dissipative term

Mitsuhiro NAKAO
Source: J. Math. Soc. Japan Volume 64, Number 3 (2012), 851-883.

#### Abstract

We derive an energy decay estimate for solutions to the initial-boundary value problem of a semilinear wave equation in exterior domains with a nonlinear localized dissipation. Our equation includes an absorbing term like |u|αu, α ≥ 0, and can be regarded as a generalized Klein-Gordon equation at least if α is closed to 0. This observation plays an essential role in our argument.

First Page:
Primary Subjects: 35B35, 35L70
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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1343133746
Digital Object Identifier: doi:10.2969/jmsj/06430851
Zentralblatt MATH identifier: 06090095
Mathematical Reviews number (MathSciNet): MR2965430

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