Global existence and asymptotic behavior of classical solutions to a fractional logistic Keller-Segel system

被引：13

作者：

Zhang, Weiyi ^{[1
]}

Liu, Zuhan ^{[1
]}

Zhou, Ling ^{[1
]}

机构：

[1] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Jiangsu, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2019年 / 189卷

基金：

中国国家自然科学基金;

关键词：

Fractional Keller-Segel system; Regularity of weak solution; Classical solution; Global existence; Asymptotic behavior; TIME BLOW-UP; PARABOLIC CHEMOTAXIS SYSTEM; PATTERN-FORMATION; WELL-POSEDNESS; BOUNDEDNESS; DIFFUSION; MODEL; LAPLACIAN; DECAY;

D O I：

10.1016/j.na.2019.111624

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider a fractional parabolic-elliptic Keller-Segel system with a logistic source on R-N. First, we establish the regularity of weak solutions of the fractional parabolic equation, using blow-up arguments combined with Liouvilletype theorems. Next, by the semigroup method and regularity results we prove the local existence and uniqueness of classical solutions. Moreover, the global existence and boundedness of classical solutions for given initial data are obtained under some conditions. Finally, we show the asymptotic behavior of the global solutions with strictly positive initial data. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页数：34

共 61 条

[41] Exponential attractor for a chemotaxis-growth system of equations [J].

Osaki, K ;

Tsujikawa, T ;

Yagi, A ;

Mimura, M .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 51 (01) :119-144

[42] Regularity theory for general stable operators [J].

Ros-Oton, Xavier ;

Serra, Joaquim .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (12) :8675-8715

[43]

Salako R. B., 2017, J DIFFER EQUATIONS, V262, P5625

[44]

Sugiyama Y, 2006, DIFFER INTEGRAL EQU, V19, P841

[45] Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term [J].

Sugiyama, Yoshie ;

Kunii, Hiroko .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 227 (01) :333-364

[46] A chemotaxis system with logistic source [J].

Tello, J. Ignacio ;

Winkler, Michael .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (06) :849-877

[47] On a quasilinear parabolic-elliptic chemotaxis system with logistic source [J].

Wang, Liangchen ;

Mu, Chunlai ;

Zheng, Pan .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (05) :1847-1872

[48] ASYMPTOTIC DECAY FOR THE CLASSICAL SOLUTION OF THE CHEMOTAXIS SYSTEM WITH FRACTIONAL LAPLACIAN IN HIGH DIMENSIONS [J].

Wang, Xi ;

Liu, Zuhan ;

Zhou, Ling .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2018, 23 (09) :4003-4020

[49] Chemotaxis with logistic source: Very weak global solutions and their boundedness properties [J].

Winkler, Michael .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 348 (02) :708-729

[50] Finite-time blow-up in low-dimensional Keller-Segel systems with logistic-type superlinear degradation [J].

Winkler, Michael .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2018, 69 (02)

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