Impulsive effects on global existence of solutions for degenerate semilinear parabolic equations
type: Item
instance of: scholarly article
title: Impulsive effects on global existence of solutions for degenerate semilinear parabolic equations
zbMATH Open document ID: 0909.35079
DOI: 10.1016/S0096-3003(96)00353-0
author: S. H. Smith
published in: Applied Mathematics and Computation
publication date: 1999-03-30T00:00:00Z
review text: The paper deals with quenching and blow-up of solutions of initial-boundary value problem for impulsive degenerate semilinear parabolic equations \[ \Biggl(x^q{\partial\over \partial t}-{\partial^2\over\partial x^2}\Biggr) u=\lambda f(u),\quad x\in(0,1),\quad (n-1)\;T< t\leq nT^-, \] \[ u(x,0)= u_0(x),\quad u(x, nT)= \sigma u(x, nT^-),\quad x\in[0, 1],\quad u(0,t)= 0= u(1,t),\quad t>0. \] The authors prove that for \(\sigma< 1\) there exists a unique critical length and study the decay of the solutions. For \(\sigma> 1\), it is proved that there exists a unique critical length, and three criteria for blow-up of solutions are obtained.
reviewed by: Emil Minchev
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35R10
zbMATH DE Number: 1183225
zbMATH Keywords: quenching
zbMATH Keywords: blow-up
zbMATH Keywords: critical length
MaRDI profile type: Publication
cites work: Q3995625
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full work available at URL: s0096-3003(96)00353-0
OpenAlex ID: W1984890890
description: scientific article; zbMATH DE number 1183225