Total blow-up versus single point blow-up
type: Item
instance of: scholarly article
title: Total blow-up versus single point blow-up
zbMATH Open document ID: 0674.35051
DOI: 10.1016/0022-0396(88)90116-7
author: A. A. Lacey
author: Jerrold W. Bebernes
author: Alberto Bressan
published in: Journal of Differential Equations
publication date: 1988-01-01T00:00:00Z
review text: The authors study blow-up of non negative solutions to a quasilinear parabolic equation describing the temperature perturbation during the ignition process of a reactive gas in a spherical container. The equation is of the form \(u_ t-\Delta u=f(u)+g(t),\) and is supplemented with zero Dirichlet boundary conditions and with a non negative initial datum which is radially symmetric and radially decreasing. The authors assume f to be differentiable and non negative for non negative arguments; g is either a non negative given function of time, or K times the space average of \(u_ t\), with \(0<K<1\). The latter assumption for g should model the compressibility of the gas. The authors provide several sufficient conditions in order blow-up to occur only at the origin, respectively everywhere. These conditions involve explicit assumptions for the function f and, in some case, on the smallness of the parameter K.
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 80A25
zbMATH DE Number: 4103597
zbMATH Keywords: blow-up
zbMATH Keywords: non negative solutions
zbMATH Keywords: quasilinear
zbMATH Keywords: temperature perturbation
zbMATH Keywords: ignition process
zbMATH Keywords: reactive gas
zbMATH Keywords: Dirichlet boundary conditions
zbMATH Keywords: initial datum
zbMATH Keywords: radially symmetric
zbMATH Keywords: radially decreasing
zbMATH Keywords: smallness of the parameter
Wikidata QID: Q59264239
MaRDI profile type: Publication
full work available at URL: 0022-0396(88)90116-7
OpenAlex ID: W2042332700
cites work: Q3710909
cites work: Thermal behavior for a confined reactive gas
cites work: Q3697477
cites work: Global existence and convergence to a singular steady state for a semilinear heat equation
cites work: Single point blow-up for a semilinear initial value problem
cites work: Q3729437
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description: scientific article; zbMATH DE number 4103597