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arXiv · 1201.4337

Stable self-similar blow up for energy subcritical wave equations

Roland Donninger·Birgit Schörkhuber
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Abstract

We consider the semilinear wave equation \[ \partial_t^2 ψ-Δψ=|ψ|^{p-1}ψ\] for $1 0$ and $κ_p$ is a $p$-dependent constant. We prove that the blow up described by $ψ^T$ is stable against small perturbations in the energy topology. This complements previous results by Merle and Zaag. The method of proof is quite robust and can be applied to other self-similar blow up problems as well, even in the energy supercritical case.

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Roland Donninger, Birgit Schörkhuber. 2012-07-11. Stable self-similar blow up for energy subcritical wave equations. https://arxiv.org/abs/1201.4337

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