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Self-similar blow up for energy supercritical semilinear wave equation

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arxiv 2211.13699 v2 pith:3EZM7QFJ submitted 2022-11-24 math.AP

Jihoi Kim This is my paper · ORCID
classification math.AP
keywords energyequationprofilesprovesemilinearsupercriticalwaveadapting
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Finite time blowup for Keller-Segel equation with logistic damping in three dimensions

    math.AP 2025-04 conditional novelty 8.0 of 10

    Finite-time blowup solutions exist for the 3D Keller-Segel equation with logistic damping for every damping coefficient below 1/3, matching the known global-existence threshold.

  2. Blow-up of the one-dimensional wave equation with quadratic spatial derivative nonlinearity

    math.AP 2025-01 conditional novelty 8.0 of 10

    Smooth solutions of u_tt - u_xx = (u_x)^2 admit stable, explicitly written blow-up profiles with logarithmic growth, and no smooth exact self-similar blow-up exists.

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