Existence problem for the Kirchhoff type wave equation with a localized weakly nonlinear dissipation in exterior domains

Jeong Ja Bae; Mitsuhiro Nakao

doi:10.3934/dcds.2004.11.731

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2004, Volume 11, Issue 2&3: 731-743. Doi: 10.3934/dcds.2004.11.731

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Existence problem for the Kirchhoff type wave equation with a localized weakly nonlinear dissipation in exterior domains

Jeong Ja Bae^1, and
Mitsuhiro Nakao^2,

1.
Department of Mathematics, University of Ulsan, Ulsan 680-749
2.
Graduate School of Mathematics, Kyushu University, Fukuoka 810-8560

Received: January 2003

Revised: March 2004

Published: September 2004

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Abstract

We prove the existence of global solutions to the initial-boundary value problem for the Kirchhoff type quasilinear wave equations in exterior domains with a localized weakly nonlinear dissipation.

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Mathematics Subject Classification: Primary: 35L70, 35L15, 65M60.

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Existence problem for the Kirchhoff type wave equation with a localized weakly nonlinear dissipation in exterior domains

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