2010年10月
Global well-posedness for the exterior initial-boundary value problem to the Kirchhoff equation
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN
- 巻
- 62
- 号
- 4
- 開始ページ
- 1167
- 終了ページ
- 1204
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.2969/jmsj/06241167
- 出版者・発行元
- MATH SOC JAPAN
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.
- リンク情報
- ID情報
-
- DOI : 10.2969/jmsj/06241167
- ISSN : 0025-5645
- Web of Science ID : WOS:000283696500006