论文标题
有限时间的标准爆炸了klein-gordon方程系统
Criteria for finite time blow up for a system of Klein-Gordon equations
论文作者
论文摘要
我们在三维欧几里得空间上对某些klein-gordon方程系统的相应解决方案爆炸的初始数据给出了三个条件。我们首先使用Levine的凹陷论点来表明能量的消极能力导致在有限的时间内炸毁当地解决方案。对于正能量的数据，我们提供了足够的条件，以使相应的解决方案在有限的时间内爆炸。这种情况以任意大能量体现基准。最后，我们使用Payne-Sattinger的潜在良好论证来将基准分类不大（准确地说，低于接地状态）分为两个部分：一个部分由基准组成，导致在有限的时间内进行爆炸解决方案，而另一部分则由导致全局解决方案的基准组成。
We give three conditions on initial data for the blowing up of the corresponding solutions to some system of Klein-Gordon equations on the three dimensional Euclidean space. We first use Levine's concavity argument to show that the negativeness of energy leads to the blowing up of local solutions in finite time. For the data of positive energy, we give a sufficient condition so that the corresponding solution blows up in finite time. This condition embodies datum with arbitrarily large energy. At last we use Payne-Sattinger's potential well argument to classify the datum with energy not so large (to be exact, below the ground states) into two parts: one part consists of datum leading to blowing-up solutions in finite time, while the other part consists of datum that leads to the global solutions.
