论文标题
紧凑型谎言组的半线性波方程
Semilinear wave equation on compact Lie groups
论文作者
论文摘要
在本说明中，我们在紧凑型谎言组上研究了具有功率非线性$ | u |^p $的半线性波方程。首先，我们通过对紧凑型谎言组的傅立叶分析证明了局部时间的存在导致能量空间。然后，在适当的符号假设下，我们证明了任何$ p> 1 $的半连接库奇问题的爆炸结果。此外，得出了局部（时间）溶液的急剧寿命估计。
In this note, we study the semilinear wave equation with power nonlinearity $|u|^p$ on compact Lie groups. First, we prove a local in time existence result in the energy space via Fourier analysis on compact Lie groups. Then, we prove a blow-up result for the semilinear Cauchy problem for any $p>1$, under suitable sign assumptions for the initial data. Furthermore, sharp lifespan estimates for local (in time) solutions are derived.
