Single-point blow-up for a semilinear parabolic system
type: Item
instance of: scholarly article
title: Single-point blow-up for a semilinear parabolic system
zbMATH Open document ID: 1171.35059
DOI: 10.4171/JEMS/145
author: Philippe Souplet
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2009-02-19T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: The authors study the positive solutions of a semilinear parabolic system coupled by power nonlinearilities in a ball or in the whole space. A single-point blow-up result is proved for a large class of radial decreasing solutions, which answer the open problem posed by \textit{A. Friedman} and \textit{Y. Giga} [J. Fac. Sci., Univ. Tokyo, Sect. I A 34, 65--79 (1987; Zbl 0648.35042)]. Finally, the author obtain the lower pointwise estimates for the final blow-up profiles.
reviewed by: Cheng He
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K35
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 5509363
zbMATH Keywords: positive solutions
zbMATH Keywords: semilinear parabolic system
zbMATH Keywords: nonlinearities
zbMATH Keywords: blow-up set
zbMATH Keywords: single point blow-up
MaRDI profile type: Publication
cites work: Liouville theorems and blow up behaviour in semilinear reaction diffusion systems
cites work: Blow-up estimates of positive solutions of a parabolic system
cites work: Convergence, asymptotic periodicity, and finite-point blow-up in one- dimensional semilinear heat equations
cites work: Q4514521
cites work: Blow-up rates for parabolic systems
description: scientific article; zbMATH DE number 5509363