Blow-up in higher-order reaction-diffusion and wave equations: how $\sqrt{log log}$ factor occurs
Analysis of PDEs
2009-01-28 v1
Abstract
The origin of non self-similar blow-up in higher-order reaction-diffusion (parabolic), wave (hyperbolic) and nonlinear dispersion equations is explained by a combination of various methods. Some links and similarities with double-log blow-up terms occurring in earlier studies of plasma physics second-order parabolic equations and the nonlinear critical Schr\"odinger equation are discussed. On the other hand, the log-log factor obtained in Petrovskii's boundary regularity study of a paraboloid vertex for the heat equation in 1934 was the first its appearance in PDE theory.
Cite
@article{arxiv.0901.4314,
title = {Blow-up in higher-order reaction-diffusion and wave equations: how $\sqrt{log log}$ factor occurs},
author = {V. A. Galaktionov},
journal= {arXiv preprint arXiv:0901.4314},
year = {2009}
}
Comments
41 pages, 10 figures