Long-time existence for semi-linear Klein-Gordon equations on tori

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:249

Article

Fang, Daoyuan¹  Zhang, Qidi^1,2 

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

[2] Univ Paris 13, Inst Galilee, CNRS, Lab Anal Geometrie & Applicat,UMR 7539, F-93430 Villetaneuse, France

关键词: Semi-linear Klein-Gordon equations;    Long-time stability;   

DOI  :  10.1016/j.jde.2010.03.025

来源: Elsevier

【 摘 要 】

We use normal forms for Sobolev energy to prove that small smooth solutions of semi-linear Klein-Gordon equations on the torus exist over a larger interval than the one given by local existence theory, for almost every value mass. The gain on the length of the lifespan does not depend on the dimension. The result relies on the fact that the difference of square of two successive distinct eigenvalues of root-Delta on T-d can be bounded from below by a constant. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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