Spectral theory and self-similar blowup in wave equations

2023/10/18 by Donninger, Roland · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2310.12016

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.

Cited by

• Stable Self-Similar Blow-Up In Nonlinear Wave Equations With Quadratic Time-Derivative Nonlinearities
• Stable Type I blow-up for the one-dimensional wave equation with time-derivative nonlinearity

Related

• Existence and stability of discretely self-similar blowup for a wave maps type equation
• Spectral Properties and Stability of Self-Similar Wave Maps
• Blow-up of the one-dimensional wave equation with quadratic spatial derivative nonlinearity
• A note on the stability of self-similar blow-up solutions for superconformal semilinear wave equations
• Stable Type I blow-up for the one-dimensional wave equation with time-derivative nonlinearity