On self-similar blow up for the energy supercritical semilinear wave equation
Journal de l’École polytechnique — Mathématiques, Volume 11 (2024), pp. 1483-1542.

We analyse the energy supercritical semilinear wave equation

Φ tt -ΔΦ-|Φ| p-1 Φ=0

in 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 [22].

Nous analysons l’équation d’onde semi-linéaire supercritique en énergie

Φ tt -ΔΦ-|Φ| p-1 Φ=0

dans l’espace d . Nous prouvons d’abord, dans un régime approprié de paramètres, l’existence d’une famille dénombrable de profils auto-similaires qui bifurquent à partir de la solution du soliton. Nous prouvons ensuite la stabilité non radiale en codimension finie de ces profils en adaptant le cadre fonctionnel de [22].

Received:
Accepted:
Published online:
DOI: 10.5802/jep.282
Classification: 35B44, 35C06, 35L05, 35L71
Keywords: Semi-linear wave equation, self-similar solution, blow up, focusing, energy super-critical, finite codimensional stability
Mot clés : Équation d’onde semi-linéaire, solution auto-similaire, explosion, supercritique en énergie, stabilité en codimension finie

Jihoi Kim 1

1 Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Jihoi Kim. On self-similar blow up for the energy supercritical semilinear wave equation. Journal de l’École polytechnique — Mathématiques, Volume 11 (2024), pp. 1483-1542. doi : 10.5802/jep.282. https://jep.centre-mersenne.org/articles/10.5802/jep.282/

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