Critical exponents and asymptotic estimates of solutions to parabolic systems with localized nonlinear sources
type: Item
instance of: scholarly article
title: Critical exponents and asymptotic estimates of solutions to parabolic systems with localized nonlinear sources
zbMATH Open document ID: 1052.35034
author: Lizhong Zhao
author: Sining Zheng
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-06T00:00:00Z
review text: The authors consider two classes of parabolic systems with localized nonlinear sources both of power and exponential types. The localized problems under consideration arise in physics and engineering, where the nonlinear reaction in dynamical system takes place only at a single site. The authors determine boundary layer profiles and blow-up rates as well.
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35K50
zbMATH DE Number: 2082196
zbMATH Keywords: critical exponents
zbMATH Keywords: parabolic systems
zbMATH Keywords: global solutions
zbMATH Keywords: blow-up
zbMATH Keywords: blow-up rates
zbMATH Keywords: boundary layers
zbMATH Keywords: asymptotic estimates
zbMATH Keywords: sources of power and exponential types
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.12.011
OpenAlex ID: W2088429730
cites work: Total blow-up versus single point blow-up
cites work: The blowup property of solutions to some diffusion equations with localized nonlinear reactions
cites work: Global existence and blow-up for a nonlinear reaction-diffusion system
cites work: Mathematical Analysis of Thermal Runaway for Spatially Inhomogeneous Reactions
cites work: Coupled diffusion systems with localized nonlinear reactions
cites work: The profile near blowup time for solutions of diffusion systems coupled with localized nonlinear reactions
cites work: Q4893660
cites work: Global existence and finite time blow up for a reaction-diffusion system
cites work: Blowup estimates for a semilinear reaction diffusion system
cites work: Blow-up in Nonlocal Reaction-Diffusion Equations
cites work: Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source
cites work: Global existence and global non-existence of solutions to a reaction-diffusion system
cites work: Nonexistence of positive solutions to a semilinear elliptic system and blow-up estimates for a reaction-diffusion system
cites work: Blow-up rates in a parabolic system of ignition model
DOI: 10.1016/J.JMAA.2003.12.011
description: scientific article; zbMATH DE number 2082196