Blowup estimates for a parabolic system in a three-species cooperating model
type: Item
instance of: scholarly article
title: Blowup estimates for a parabolic system in a three-species cooperating model
zbMATH Open document ID: 1052.35081
author: Kwang Ik Kim
author: Zhigui Lin
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-06T00:00:00Z
review text: The authors study the blow-up estimates for the solutions of the following semilinear parabolic system \[ \begin{alignedat}{3} &u_{1t}- d_1 \Delta u_1= u_1(a_1- c_1u_1+ e_1u_2) && &\quad\text{in } &\Omega\times (0,T),\\ &u_{2t}- d_2 \Delta u_2= u_2 (a_2+ b_2u_1- c_2u_2+ e_2u_3) && &\quad\text{in } &\Omega\times (0,T),\\ &u_{3t}- d_3 \Delta u_3= u_3(a_3+ b_3u_2- c_3u_3) && &\quad\text{in }&\Omega\times (0,T),\\ &u_i(x,t)= 0 &\text{for }&i=1,2,3 &\quad \text{on } &\partial\Omega\times (0,T),\\ &u_i(x,0)= u_{i,0}(x) \quad &\text{for }&i=1,2,4 &\quad \text{in }&\Omega. \end{alignedat} \] The authors derive the upper and lower bound for blow-up rates in the case \(N=1\). Note that \(\Omega\) is a bounded domain in \(\mathbb{R}^n\) with smooth boundary \(\partial\Omega\). Moreover the comparison principle for a bounded and unbounded domain are given and the corresponding scalar problem is studied.
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 2082170
zbMATH Keywords: upper and lower bounds
zbMATH Keywords: comparison principle
zbMATH Keywords: bounded and unbounded domain
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.01.026
OpenAlex ID: W1979491228
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DOI: 10.1016/J.JMAA.2004.01.026
description: scientific article; zbMATH DE number 2082170