Threshold for blowup for the supercritical cubic wave equation

Autor(en)

Irfan Glogić, Maciej Maliborski, Birgit Schörkhuber

Abstrakt

We consider the focusing cubic wave equation in the energy supercritical case, i.e. in dimensions . For this model an explicit nontrivial self-similar 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.

Organisation(en)

Institut für Mathematik, Gravitationsphysik

Externe Organisation(en)

Karlsruher Institut für Technologie

Journal

Nonlinearity

Band

33

Seiten

2143-2158

Anzahl der Seiten

16

ISSN

0951-7715

DOI

https://doi.org/10.1088/1361-6544/ab6f4d

Publikationsdatum

03-2020

Peer-reviewed

Ja

ÖFOS 2012

101002 Analysis, 103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Allgemeine Physik und Astronomie, Applied Mathematics, Statistical and Nonlinear Physics, Mathematical Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/58457346-6cc0-4ec3-9f79-a5b275783c39