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Co-dimension one stable blowup for the supercritical cubic wave equation

Glogić, Irfan; Schörkhuber, Birgit

Abstract:
For the focusing cubic wave equation, we find an explicit, non-trivial self-similar blowup solution u^∗_T , which is defined on the whole space and exists in all supercritical dimensions d ≥ 5. For d = 7, we analyze its stability properties without any symmetry assumptions and prove the existence of a co-dimension one Lipschitz manifold consisting of initial data whose solutions blowup in finite time and converge asymptotically to u^∗_T (modulo space-time shifts and Lorentz boosts) in the backward lightcone of the blowup point. The underlying topology is strictly above scaling.

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Volltext §
DOI: 10.5445/IR/1000088078
Veröffentlicht am 03.12.2018
Coverbild
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
urn:nbn:de:swb:90-880786
KITopen-ID: 1000088078
Verlag KIT, Karlsruhe
Umfang 47 S.
Serie CRC 1173 ; 2018/39
Projektinformation SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015)
Schlagworte nonlinear wave equation, supercritical, blowup, self-similar, stability
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