Self-similar blow up for energy supercritical semilinear wave equation

Jihoi Kim

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arXiv · 2211.13699

Self-similar blow up for energy supercritical semilinear wave equation

Jihoi Kim

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Abstract

We analyse the energy supercritical semilinear wave equation $$\Phi_{tt}-\Delta\Phi-|\Phi|^{p-1}\Phi=0$$ in $\mathbb R^d$ space. We first prove in a suitable regime of parameters the existence of a countable family of self similar profiles which bifurcate from the soliton solution. We then prove the non radial finite codimensional stability of these profiles by adapting the functional setting of arXiv:1912.11005.

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Jihoi Kim. 2022-11-24. Self-similar blow up for energy supercritical semilinear wave equation. https://arxiv.org/abs/2211.13699

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