散射情形下次 Strauss 指数半线性阻尼波动方程的爆破
偏微分方程分析
2018-03-01 v3
摘要
众所周知，当阻尼有效时，半线性阻尼波动方程的临界指数是 Fujita 指数。Lai、Takamura 和 Wakasa 于 2017 年得到了一个爆破结果，不仅针对超 Fujita 指数，还针对与 Strauss 指数密切相关的指数，此时阻尼是标度不变的且其常数相对较小，这一结果最近被 Ikeda 和 Sobajima 推广。通过为未知函数空间积分的时间导数引入一个乘子，我们成功运用了半线性波动方程的分析技术，并证明了当阻尼处于散射范围时，次 Strauss 指数半线性阻尼波动方程的爆破结果。
引用
@article{arxiv.1707.09583,
title = {Blow-up for semilinear damped wave equations with sub-Strauss exponent in the scattering case},
author = {Ning-An Lai and Hiroyuki Takamura},
journal= {arXiv preprint arXiv:1707.09583},
year = {2018}
}
备注
The first version had the critical case, but there was a gap in the proof. That part was removed. The improvements of the estimates of the lifespan in low dimensions are added as in Theorem2.2 and Theorem 2.3 to the second version