Blow-up with logarithmic nonlinearities
type: Item
instance of: scholarly article
title: Blow-up with logarithmic nonlinearities
zbMATH Open document ID: 1133.35059
author: Raúl Ferreira
author: Arturo de Pablo
author: J. D. Rossi
published in: Journal of Differential Equations
publication date: 2007-09-13T00:00:00Z
full work available at URL: 2007blowup-04.pdf
review text: The authors study nonnegative solutions of the nonlinear diffusion equation \[ u_t=u_{xx}-\lambda(u+1)\log^p(u+1) \] in the half-line \((0,\infty)\) under the nonlinear boundary condition \[ -u_x(0,t)=\lambda(u+1)\log^q(u+1)(0,t) \] and a suitable initial condition. They determine the ranges of positive parameters \(p\), \(q\) and \(\lambda\) for which the solution is global in time and ranges for which it blows up in finite time. For blow-up solutions the blow-up rate and the blow-up set are found and the asymptotic behaviour close to the blow-up time is described. The appearance of extinction in finite time is also studied.
reviewed by: Peter Poláčik
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 5190783
zbMATH Keywords: nonlinear boundary conditions
zbMATH Keywords: blow-up rate
zbMATH Keywords: blow-up set
zbMATH Keywords: extinction
MaRDI profile type: Publication
OpenAlex ID: W2143512364
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DOI: 10.1016/J.JDE.2007.05.004
description: scientific article; zbMATH DE number 5190783