KIT | KIT-Bibliothek | Impressum | Datenschutz

Threshold for blowup for the supercritical cubic wave equation

Glogić, Irfan; Maliborski, Maciej; Schörkhuber, Birgit

Abstract:
We consider the focusing cubic wave equation in the energy supercritical case, i.e. in dimensions d ≥¬ 5. For this model an explicit nontrivial selfsimilar blowup solution was recently found by the first and third author in Glogić and Schörkhuber (2018 (arXiv:1810.07681)). Furthermore, the solution is proven to be co-dimension one stable in d = 7. In this paper, we study the equation from a numerical point of view. For d = 5 and d = 7 in the radial case, we provide evidence that this solution is at the threshold between generic ODE blowup and dispersion. In addition, we investigate the spectral problem that underlies the stability analysis and compute the spectrum in general supercritical dimensions.

Open Access Logo


Verlagsausgabe §
DOI: 10.5445/IR/1000118878
Veröffentlicht am 30.04.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 05.2020
Sprache Englisch
Identifikator ISSN: 0951-7715, 1361-6544
KITopen-ID: 1000118878
Erschienen in Nonlinearity
Band 33
Heft 5
Seiten 2143–2158
Vorab online veröffentlicht am 16.03.2020
Schlagwörter nonlinear wave equation, focusing, self-similar blowup, threshold, stability
Nachgewiesen in Scopus
Web of Science
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page