Anomalous solutions to nonlinear hyperbolic equations
Analysis of PDEs
2022-08-15 v2
Abstract
The behavior of sufficiently regular solutions to semilinear hyperbolic equations has attracted a great deal of attention in the past decades, concerning local/global existence, finite time blow-up, critical exponents, and propagation of singularities. Solutions of lower regularity may exhibit unexpected (anomalous) propagation of singularities. The purpose of this paper is to present various striking examples that seemingly have not been addressed in the literature so far. The key issue is the interpretation of the nonlinear operations.
Keywords
Cite
@article{arxiv.2002.05081,
title = {Anomalous solutions to nonlinear hyperbolic equations},
author = {Michael Oberguggenberger},
journal= {arXiv preprint arXiv:2002.05081},
year = {2022}
}