含乘积型半线性项的一维波动方程的广义组合效应
偏微分方程分析
2024-05-30 v2
摘要
我们关注一维空间半线性波动方程中两类不同非线性项的所谓“组合效应”。最近，当且仅当初始速度的总积分为零（即 Huygens 原理成立）时，已获得了与高维情形同样表述的首个结果。在本文中，我们将非线性项推广到包含乘积型的一般形式。此类模型方程仅在一维空间中极有意义，因为高维中的大多数情形在非线性波动方程的一般理论中具有经典解的全局时间存在性。同样值得注意的是，我们在解的生命周期估计上的结果部分优于一般理论。这一事实告诉我们，有可能改进三十多年前被认为已完备的一般理论。
引用
@article{arxiv.2305.00180,
title = {The generalized combined effect for one dimensional wave equations with semilinear terms including product type},
author = {Ryuki Kido and Takiko Sasaki and Shu Takamatsu and Hiroyuki Takamura},
journal= {arXiv preprint arXiv:2305.00180},
year = {2024}
}
备注
The first version has a wrong citation of the result of the general theory by [12,13] at the last line in (2.24). This part is corrected. As a result, the possibility to improve the general theory may happen only for the combined effected case as stated this version. This kind of error is also found in the previous work in arXiv:2205.07198