个人信息Personal Information
教授
博士生导师
硕士生导师
性别:男
毕业院校:吉林大学
学位:博士
所在单位:数学科学学院
学科:基础数学
办公地点:创新园大厦 A1032
电子邮箱:snzheng@dlut.edu.cn
Asymptotic behaviour of solutions to the Keller-Segel model for chemotaxis with prevention of overcrowding
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论文类型:期刊论文
发表时间:2013-02-01
发表刊物:NONLINEARITY
收录刊物:SCIE、Scopus
卷号:26
期号:2
页面范围:405-416
ISSN号:0951-7715
摘要:This paper deals with the Keller-Segel chemotaxis model of parabolic-elliptic type with the volume-filling effect studied by Burger et al (2006 The Keller-Segel model for chemotaxis with prevention of overcrowding: linear versus nonlinear diffusion SIAM J. Math. Anal. 38 1288-315). In their discussion on the large time asymptotic behaviour of solutions, the diffusion rate of rho (the density of cells) had to be assumed to be large with epsilon > 1/4. While for the nonlinear diffusion model, it was proved that the asymptotic behaviour of solutions is fully determined by the diffusion constant being larger or smaller than the threshold value epsilon = 1. The same 'large epsilon-restriction' (epsilon > 1/4) was also made for studying the parallel parabolic-parabolic model in Di Francesco and Rosado (2008 Fully parabolic Keller-Segel model for chemotaxis with prevention of overcrowding Nonlinearity 21 2715-30), where it was pointed out that 'Whether this condition is necessary to have large time decay (and consequently a self-similar behaviour) for rho is still an open problem even in the (simpler) parabolic-elliptic case'. The aim of the paper is to answer this problem for the parabolic-elliptic model. We prove the mentioned time decay estimate without the restriction epsilon > 1/4. The main technique used in this paper is the L-p-L-q estimate method.