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arXiv · 1909.01626

Dynamics at the threshold for blowup for supercritical wave equations outside a ball

Piotr Bizoń·Maciej Maliborski
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Abstract

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.

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Piotr Bizoń, Maciej Maliborski. 2019-09-04. Dynamics at the threshold for blowup for supercritical wave equations outside a ball. https://doi.org/10.1088/1361-6544/ab8352

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