Global solvability for the Kirchhoff equations in exterior domains of dimension larger than three

✍ Scribed by Taeko Yamazaki

• Publisher: John Wiley and Sons
• Year: 2004
• Tongue: English
• Weight: 200 KB
• Volume: 27
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.530

✦ Synopsis

Abstract

We consider the unique global solvability of initial (boundary) value problem for the Kirchhoff equations in exterior domains or in the whole Euclidean space for dimension larger than three. The following sufficient condition is known: initial data is sufficiently small in some weighted Sobolev spaces for the whole space case; the generalized Fourier transform of the initial data is sufficiently small in some weighted Sobolev spaces for the exterior domain case. The purpose of this paper is to give sufficient conditions on the usual Sobolev norm of the initial data, by showing that the global solvability for this equation follows from a time decay estimate of the solution of the linear wave equation. Copyright © 2004 John Wiley & Sons, Ltd.