Blow-up for a three dimensional Keller-Segel model with consumption of chemoattractant

被引：13

作者：

Jiang, Jie ^{[1
]}

Wu, Hao ^{[2
,3
]}

Zheng, Songmu ^{[2
]}

机构：

[1] Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Hubei, Peoples R China

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[3] Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2018年 / 264卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Chemotaxis; Classical solutions; Blow-up criterion; Blow-up rate; CHEMOTAXIS-STOKES SYSTEM; GLOBAL EXISTENCE; NONLINEAR DIFFUSION; EVENTUAL SMOOTHNESS; BOUNDEDNESS; BEHAVIOR; STABILIZATION; EQUATIONS; DECAY;

D O I：

10.1016/j.jde.2018.01.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate blow-up properties for the initial-boundary value problem of a Keller-Segel model with consumption of chemoattractant when the spatial dimension is three. Through a kinetic reformulation of the Keller-Segel system, we first derive some higher-order estimates and obtain certain blow-up criteria for the local classical solutions. These blow-up criteria generalize the results in [4,5] from the whole space R-3 to the case of bounded smooth domain Omega subset of R-3. Lower global blow-up estimate on parallel to n parallel to (infinity)(L)((Omega)) is also obtained based on our higher-order estimates. Moreover, we prove local non-degeneracy for blow-up points. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：5432 / 5464

页数：33

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