Improved Kato's lemma on ordinary differential inequality and its application to semilinear wave equations
Abstract
We are interested in the upper bound of the lifespan of solutions of semilinear wave equations from above. For the sub-critical case in high dimensions, it has been believed that the basic tools of its analysis are Kato's lemma on ordinary differential inequalities and the rescaling argument in the functional method. But there is a small lack of delicate analysis and no published paper about this. Here we give a simple alternative proof by means of improved Kato's lemma without any rescaling argument.
Keywords
Cite
@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}
}
Comments
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