外域中非线性波动方程全局存在性的一个初等证明
偏微分方程分析
2009-09-01 v2
摘要
本文旨在给出外域中满足零条件(null condition)的非线性波动方程全局存在性结果的一个初等证明。我们证明的新颖之处在于,通过使用关于光锥切向导数的一组新的加权逐点估计,完全避免了缩放算子的使用——在混合问题中,缩放算子会使论证变得复杂。
引用
@article{arxiv.0706.1833,
title = {An elementary proof of global existence for nonlinear wave equations in an exterior domain},
author = {Soichiro Katayama and Hideo Kubo},
journal= {arXiv preprint arXiv:0706.1833},
year = {2009}
}
备注
(i) To simplify the proof of Theorems 4.1 and 4.2 in the previous version, we added Lemma 4.1. (ii) Proof of the theorem for general situation of the multiple speeds are given, while it was proved only for the single speed case in the previous version. (iii) (3.2) is replaced by its accurate form. (iv) Some refernces are added, and many typos are corrected