Blow-up in higher-order reaction-diffusion and wave equations: how $\sqrt{log log}$ factor occurs

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dc.creatorGalaktionov, V. A.
dc.date2009-01-27
dc.date.accessioned2026-07-07T12:34:56Z
dc.date.available2026-07-07T12:34:56Z
dc.descriptionThe 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 Schrödinger 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.
dc.description41 pages, 10 figures
dc.identifierhttps://arxiv.org/abs/0901.4314
dc.identifierhttp://arxiv.org/abs/0901.4314
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217617
dc.subjectAnalysis of PDEs
dc.subject35K55, 35K40
dc.titleBlow-up in higher-order reaction-diffusion and wave equations: how $\sqrt{log log}$ factor occurs
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