Blow-up of solutions of nonlinear degenerate parabolic equations
type: Item
instance of: scholarly article
title: Blow-up of solutions of nonlinear degenerate parabolic equations
zbMATH Open document ID: 0619.35060
DOI: 10.1007/BF00251413
author: A. Friedman
author: J. B. McLeod
published in: Archive for Rational Mechanics and Analysis
publication date: 1986-01-01T00:00:00Z
review text: The authors consider the global existence of solutions of the parabolic initial-boundary value problem \[ u_ t=u^ 2(\Delta u+u),\quad (x\in \Omega,\quad t>0);\quad u=0,\quad (x\in \partial \Omega,\quad t>0);\quad u(x,0)=\phi (x)\geq 0;\quad (x\in \Omega) \] where \(\Omega\) is a bounded domain in \({\mathbb{R}}^ n\). They prove rigorous results concerning the blow-up set and in particular, prove that the blow-up set is \(\{\) x: - \(\pi\) /2\(\leq x\leq \pi /2\}\) in the case n-1 and \(\phi\) even. The techniques employed extend to a wide variety of nonlinear parabolic equations.
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 4004752
zbMATH Keywords: resistive diffusion
zbMATH Keywords: force-free magnetic field
zbMATH Keywords: plasma
zbMATH Keywords: global existence
zbMATH Keywords: parabolic initial-boundary value problem
zbMATH Keywords: bounded domain
zbMATH Keywords: blow-up set
zbMATH Keywords: nonlinear parabolic equations
MaRDI profile type: Publication
cites work: Q5520962
cites work: Q3697477
cites work: Nonlinear classical diffusion in a contained plasma
cites work: Q5596448
cites work: Single point blow-up for a semilinear initial value problem
full work available at URL: https://doi.org/10.1007/bf00251413
OpenAlex ID: W2071389282
description: scientific article; zbMATH DE number 4004752