论文标题
紧凑型谎言组的非线性分数阻尼波方程
Nonlinear fractional damped wave equation on compact Lie groups
论文作者
论文摘要
在本文中，我们处理了一个紧凑的谎言组$ g $上的初始值分数阻尼波方程，具有功率类型的非线性。该手稿的目的是双重的。首先，使用对紧凑型谎言组的傅立叶分析，我们证明了局部时间的存在导致$ g $上的分数阻尼波方程的能量空间。此外，在初始数据的一定条件下，建立了有限的时间爆破结果。在本文的下一部分中，我们考虑具有较低阶段的分数波方程，即紧凑型谎言组上具有相同功率类型的非线性的阻尼和质量，并证明能量演化空间中小数据解决方案的全球及时存在。
In this paper, we deal with the initial value fractional damped wave equation on $G$, a compact Lie group, with power-type nonlinearity. The aim of this manuscript is twofold. First, using the Fourier analysis on compact Lie groups, we prove a local in-time existence result in the energy space for the fractional damped wave equation on $G$. Moreover, a finite time blow-up result is established under certain conditions on the initial data. In the next part of the paper, we consider fractional wave equation with lower order terms, that is, damping and mass with the same power type nonlinearity on compact Lie groups, and prove the global in-time existence of small data solutions in the energy evolution space.
