Spectral theory and self-similar blowup in wave equations
Analysis of PDEs
2024-03-20 v2 Mathematical Physics
math.MP
Spectral Theory
Abstract
This is an expository article that describes the spectral-theoretic aspects in the study of the stability of self-similar blowup for nonlinear wave equations. The linearization near a self-similar solution leads to a genuinely nonself-adjoint operator which is difficult to analyze. The main goal of this article is to provide an accessible account to the only known method that is capable of providing sufficient spectral information to complete the stability analysis. The exposition is based on a mini course given at the Summer School on Geometric Dispersive PDEs in Obergurgl, Austria, in September 2022.
Keywords
Cite
@article{arxiv.2310.12016,
title = {Spectral theory and self-similar blowup in wave equations},
author = {Roland Donninger},
journal= {arXiv preprint arXiv:2310.12016},
year = {2024}
}
Comments
Some minor improvements based on the referees' comments, will appear in Bulletin of the AMS