论文标题
全球存在和有限的时间爆破，用于持续平均曲率的H系统热流动
Global existence and finite time blow-up for the heat flow of H-system with constant mean curvature
论文作者
论文摘要
在本文中，我们使用修改后的潜在良好方法来研究在$ r^2 $的有界平滑域中H-System热流的长期行为。当初始能源在三种情况下，证明了解决方案的全球存在和有限的时间爆炸。当初始能源低或关键时，我们不仅给全球存在和解决方案的爆炸带来了阈值，而且还获得了全球解决方案的$ l^2 $ norm norm的衰减率。当初始能量很高时，还提供了足够的全球存在条件和解决方案的爆炸。我们扩展了[12]中获得的最新结果。
In this paper, we use the modified potential well method to study the long time behaviors of solutions to the heat flow of H-system in a bounded smooth domain of $R^2$. Global existence and finite time blowup of solutions are proved when the initial energy is in three cases. When the initial energy is low or critical, we not only give a threshold result for the global existence and blowup of solutions, but also obtain the decay rate of the $L^2$ norm for global solutions. When the initial energy is high, sufficient conditions for the global existence and blowup of solutions are also provided. We extend the recent results which were obtained in [12].
