ALMOST GLOBAL EXISTENCE FOR THE KLEIN-GORDON EQUATION WITH THE KIRCHHOFF-TYPE NONLINEARITY

被引：0

作者：

Han, Zheng ^{[1
]}

Fang, Daoyuan ^{[2
]}

机构：

[1] Hangzhou Normal Univ, Dept Math, Hangzhou 311121, Peoples R China

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

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2021年 / 20卷 / 02期

关键词：

Almost global existence; Klein-Gordon equation; Kirchhoff-type non-linearity; normal forms; LONG-TIME EXISTENCE; WELL-POSEDNESS;

D O I：

10.3934/cpaa.2020287

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove an almost global existence result for the Klein-Gordon equation with the Kirchhoff-type nonlinearity on T-d with Cauchy data of small amplitude epsilon. We show a lower bound epsilon(-)(2N)(-2) for the existence time with any natural number N. The proof relies on the method of normal forms and induction. The structure of the nonlinearity is good enough that proceeds normal forms up to any order.

引用

页码：737 / 754

页数：18

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