改进的关于常微分不等式的 Kato 引理及其在半线性波动方程中的应用
偏微分方程分析
2018-03-01 v3
摘要
我们关注半线性波动方程解的生命周期上界。对于高维次临界情形，人们一直认为其分析的基本工具是关于常微分不等式的 Kato 引理和泛函方法中的重标度论证。但此前缺乏精细的分析且尚无相关论文发表。在此，我们利用改进的 Kato 引理给出了一种简单的替代证明，无需任何重标度论证。
引用
@article{arxiv.1412.2550,
title = {Improved Kato's lemma on ordinary differential inequality and its application to semilinear wave equations},
author = {Hiroyuki Takamura},
journal= {arXiv preprint arXiv:1412.2550},
year = {2018}
}
备注
20 pages. In the second version, the assumption of Lemma 2.2 is improved. As a result, the restriction in low dimensions in Theorem 3.2 is removed. Finally, I have submitted the third version here which is accepted for publication in the journal, Nonlinear Analysis TMA. It has minor corrections and the proof of Theorem 4.1 is rewritten more clearly