We consider spherically symmetric supercritical focusing wave equations outside a ball. Using mixed analytical and numerical methods, we show that the threshold for blowup is given by a codimension-one stable manifold of the unique static solution with exactly one unstable direction. We analyze in detail the convergence to this critical solution for initial data fine-tuned to the threshold.

中文翻译：

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球外超临界波动方程爆破阈值的动力学

我们考虑球外的球对称超临界聚焦波动方程。使用混合的分析和数值方法，我们表明膨胀的阈值是由唯一静态解的一个共维一稳定流形给出的，只有一个不稳定方向。我们详细分析了对初始数据微调到阈值的关键解决方案的收敛性。