Lower bound of the lifespan of solutions to semilinear wave equations in an exterior domain
Lower bound of the lifespan of solutions to semilinear wave equations in an exterior domain
复制标题
外域半线性波动方程解的寿命下界
DOI：
10.1142/s0219891613500094
复制
发表时间：
2013
影响因子：
0.7
通讯作者：
Soichiro Katayama and Hideo Kubo
中科院分区：
文献类型：
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作者：
Soichiro Katayama;Hideo Kubo and Sandra Lucente;Soichiro Katayama;Soichiro Katayama and Hideo Kubo
本文研究了三维空间区域上半线性波动方程的Cauchy-Dirichlet问题，该区域位于有界非捕获障碍物的外部。当初始数据的大小趋于零时，我们得到了经典解的寿命下限的详细估计，这与John和Hörmander处理Cauchy问题的工作类似。我们表明，我们的估计是尖锐的径向对称的情况下，至少。
We consider the Cauchy–Dirichlet problem for semilinear wave equations in a three space-dimensional domain exterior to a bounded and non-trapping obstacle. We obtain a detailed estimate for the lower bound of the lifespan of classical solutions when the size of initial data tends to zero, in a similar spirit to that of the works of John and Hörmander where the Cauchy problem was treated. We show that our estimate is sharp at least for radially symmetric case.