Blow-up criteria for the classical Keller-Segel model of chemotaxis in higher dimensions

被引：6
作者：
Naito, Yuki [1 ]
机构：
[1] Hiroshima Univ, Dept Math, Higashihiroshima 7398526, Japan
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年 / 297卷
关键词：
Chemotaxis; Blow-up of solutions; Global existence of solutions; CAUCHY-PROBLEM; DIFFUSION; ATTRACTION;
D O I：
10.1016/j.jde.2021.06.024
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the simplest parabolic-elliptic model of chemotaxis in space dimensions N >= 3, and show the optimal conditions on the initial data for the finite time blow-up and the global existence of solutions in terms of stationary solutions. Our argument is based on the study of the Cauchy problem for the transformed equation involving the averaged mass of the solution. (C) 2021 Elsevier Inc. All rights reserved.
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页码：144 / 174
页数：31
相关论文
共 20 条
[1]  
[Anonymous], 1998, Adv. Differ. Equ
[2]  
BILER P, 1995, STUD MATH, V114, P181
[3]  
BILER P, 1994, C MATH, V66, P319
[4]  
Biler P., 2019, SERIES MATH BIOL SCI SERIES MATH BIOL SCI
[5]  
BILER P, 1995, C MATH, V68, P229
[6]   Global radial solutions in classical Keller-Segel model of chemotaxis [J].
Biler, Piotr ;
Karch, Grzegorz ;
Pilarczyk, Dominika .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 267 (11) :6352-6369
[7]   Blowing up radial solutions in the minimal Keller-Segel model of chemotaxis [J].
Biler, Piotr ;
Zienkiewicz, Jacek .
JOURNAL OF EVOLUTION EQUATIONS, 2019, 19 (01) :71-90
[8]   Large global-in-time solutions to a nonlocal model of chemotaxis [J].
Biler, Piotr ;
Karch, Grzegorz ;
Zienkiewicz, Jacek .
ADVANCES IN MATHEMATICS, 2018, 330 :834-875
[9]   MORREY SPACES NORMS AND CRITERIA FOR BLOWUP IN CHEMOTAXIS MODELS [J].
Biler, Piotr ;
Karch, Grzegorz ;
Zienkiewicz, Jacek .
NETWORKS AND HETEROGENEOUS MEDIA, 2016, 11 (02) :239-250
[10]   Optimal criteria for blowup of radial and N-symmetric solutions of chemotaxis systems [J].
Biler, Piotr ;
Karch, Grzegorz ;
Zienkiewicz, Jacek .
NONLINEARITY, 2015, 28 (12) :4369-4387
12