A note on quenching for parabolic equations with dynamic boundary conditions
type: Item
instance of: scholarly article
title: A note on quenching for parabolic equations with dynamic boundary conditions
zbMATH Open document ID: 1056.35089
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-09-23T00:00:00Z
review text: The author considers the semilinear parabolic equation \(u_t- \Delta u= g(u)\) in for \(x\in\Omega\) and \(t> 0\) under the dynamic boundary condition \(u_t+ u_\nu= g(u)\) for \(x\in\partial\Omega\) and \(t> 0\) and under initial datum \(u(x, 0)= u_0(x)\). Here \(\Omega\) is a bounded domain, \(\nu\) is the exterior normal and \(g\) is positive near zero and blows up at some finite \(b\). If \(u(x, t)\) reaches \(b\), it quenches. The main result states that under suitable assumptions \(u\) quenches in finite time \(T\) and that this time can be estimated in terms of the data.
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 2102593
zbMATH Keywords: semilinear parabolic equation
author: Joakim Petersson
MaRDI profile type: Publication
full work available at URL: j.na.2004.01.006
OpenAlex ID: W2037026001
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cites work: Q4224949
cites work: On solutions of initial -boundary problem for \(u_t=u_{xx}+1/(1-u)\)
cites work: Q4027434
DOI: 10.1016/J.NA.2004.01.006
description: scientific article; zbMATH DE number 2102593