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October, 2010 Global well-posedness for the exterior initial-boundary value problem to the Kirchhoff equation
Tokio MATSUYAMA
J. Math. Soc. Japan 62(4): 1167-1204 (October, 2010). DOI: 10.2969/jmsj/06241167

Abstract

The aim of this paper is to find a general class of data in which the global well-posedness for the exterior initial-boundary value problem to the Kirchhoff equation is assured. The result obtained in the present paper will be applied to the existence of scattering states. A class of weighted Sobolev spaces will be also presented in which the global well-posedness is assured. For this purpose, the method of generalized Fourier transforms is developed for some oscillatory integral associated with this equation. The crucial point is to obtain the resolvent expansion of the minus Laplacian around the origin in C, and the differentiability of the generalized Fourier transforms.

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Tokio MATSUYAMA. "Global well-posedness for the exterior initial-boundary value problem to the Kirchhoff equation." J. Math. Soc. Japan 62 (4) 1167 - 1204, October, 2010. https://doi.org/10.2969/jmsj/06241167

Information

Published: October, 2010
First available in Project Euclid: 2 November 2010

zbMATH: 1223.35238
MathSciNet: MR2761918
Digital Object Identifier: 10.2969/jmsj/06241167

Subjects:
Primary: 35L05
Secondary: 35L10

Keywords: Generalized Fourier transform , Kirchhoff equation , scattering theory

Rights: Copyright © 2010 Mathematical Society of Japan

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Vol.62 • No. 4 • October, 2010
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