论文标题
在对紧凑型谎言组中功率非线性的半连接阻尼波方程的解决方案爆炸
On the blow-up of solutions to semilinear damped wave equations with power nonlinearity in compact Lie groups
论文作者
论文摘要
在本说明中，我们证明了一个紧凑的谎言组中半连接抑制的波动方程的爆炸结果，在适当的积分符号假设下，使用迭代参数，具有任何$ p> 1 $的功率非线性$ | u | u |^p $。该方法的副产品是局部时间溶液寿命的上限估计值。作为初步结果，通过对紧凑型谎言组的傅立叶分析证明了局部（及时的）存在结果。
In this note, we prove a blow-up result for the semilinear damped wave equation in a compact Lie group with power nonlinearity $|u|^p$ for any $p>1$, under suitable integral sign assumptions for the initial data, by using an iteration argument. A byproduct of this method is the upper bound estimate for the lifespan of a local in time solution. As a preliminary result, a local (in time) existence result is proved in the energy space via Fourier analysis on compact Lie groups.
