Numerical blow-up time for a semilinear parabolic equation with nonlinear boundary conditions
type: Item
instance of: scholarly article
title: Numerical blow-up time for a semilinear parabolic equation with nonlinear boundary conditions
zbMATH Open document ID: 1179.35168
DOI: 10.1155/2008/753518
author: Louis A. Assalé
author: Diabate Nabongo
author: Théodore K. Boni
published in: Journal of Applied Mathematics
publication date: 2009-11-10T00:00:00Z
full work available at URL: https://eudml.org/doc/45748
review text: Summary: We obtain some conditions under which the positive solution for semidiscretizations of the semilinear equation \(u_{t}=u_{xx} - a(x,t)f(u)\), \(0<x<1\), \(t\in (0,T)\), with boundary conditions \(u_{x}(0,t)=0\), \(u_{x}(1,t)=b(t)g(u(1,t))\), blows up in a finite time and estimate its semidiscrete blow-up time. We also establish the convergence of the semidiscrete blow-up time and obtain some results about numerical blow-up rate and set. Finally, we get an analogous result taking a discrete form of the above problem and give some computational results to illustrate some points of our analysis.
Mathematics Subject Classification ID: 35K58
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 5628315
zbMATH Keywords: one space dimension
zbMATH Keywords: positive solution
zbMATH Keywords: semidiscretizations
Wikidata QID: Q58645966
MaRDI profile type: Publication
OpenAlex ID: W2067588726
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description: scientific article; zbMATH DE number 5628315