Dynamics at the threshold for blowup for supercritical wave equations outside a ball

Author(s)
Piotr Bizoń, Maciej Maliborski
Abstract

We consider spherically symmetric supercritical focusing wave equations outside a ball. Using mixed analytical and numerical methods, we show that the threshold for blowup is given by a codimension-one stable manifold of the unique static solution with exactly one unstable direction. We analyse in detail the convergence to this critical solution for initial data fine-tuned to the threshold.

Organisation(s)
Gravitational Physics
External organisation(s)
Jagiellonian University in Krakow
Journal
Nonlinearity
Volume
33
Pages
3195-3205
No. of pages
11
ISSN
0951-7715
DOI
https://doi.org/10.1088/1361-6544/ab8352
Publication date
05-2020
Peer reviewed
Yes
Austrian Fields of Science 2012
103036 Theoretical physics
Keywords
ASJC Scopus subject areas
Statistical and Nonlinear Physics, Mathematical Physics, Physics and Astronomy(all), Applied Mathematics
Portal url
https://ucrisportal.univie.ac.at/en/publications/dynamics-at-the-threshold-for-blowup-for-supercritical-wave-equations-outside-a-ball(fceff2a7-39c6-418f-9bce-a1c79d2eade1).html