带有Logistic源的吸引-排斥趋化性系统的整体有界性和渐近行为

数学物理学报 ›› 2017, Vol. 37 ›› Issue (1): 113-121.

带有Logistic源的吸引-排斥趋化性系统的整体有界性和渐近行为

郜欣春¹, 周健¹, 田苗青^1,2

1. 郑州大学西亚斯国际学院文理学院河南新郑 451150;
2. 大连理工大学数学与科学学院辽宁大连 116024

收稿日期:2016-05-23 修回日期:2016-10-21 出版日期:2017-02-26 发布日期:2017-02-26
通讯作者: 田苗青 E-mail:npctian@126.com
作者简介:郜欣春,E-mail:gxc3270@163.com;周健,E-mail:gudanzj@163.com
基金资助:
河南省科技攻关项目（162102210103）

Global Boundedness and Asymptotic Behavior in an Attraction-Repulsion Chemotaxis System with Logistic Source

Gao Xinchun¹, Zhou Jian¹, Tian Miaoqing^1,2

1. School of Arts and Science, Sias International University, Henan Xinzheng 451150;
2. School of Mathematical Sciences, Dalian University of Technology, Liaoning Dalian 116024

Received:2016-05-23 Revised:2016-10-21 Online:2017-02-26 Published:2017-02-26
Supported by:
Supported by the Science and Technology Project of Henan Province (162102210103)

摘要/Abstract

摘要：

该文研究了有界区域Ω⊂R^N（N≥1）中，齐次Neumann边值条件下带有Logistic源的吸引-排斥趋化性系统u_t=Δu-▽·（u▽v）+μ₁u（1-u），0=Δv+w-v，w_t=Δw+▽·（w▽z）+μ₂w（1-w），0=Δz-z+u，其中μ₁，μ₂>0.证明了对任何非负初值u₀（x），w₀（x）∈C（Ω），解（u（·，t），v（·，t），w（·，t），z（·，t））整体有界.此外，如果μ₁，μ₂>（1）/（16），那么当t→∞时，解（u（·，t），v（·，t），w（·，t），z（·，t））在L^∞模意义下渐近收敛于常数平衡解（1，1，1，1）.

关键词: 吸引-排斥, 趋化性, Logistic源, 有界性, 渐近行为

Abstract:

This paper studies the attraction-repulsion chemotaxis system with logistic source u_t=Δu-▽·(u▽v)+μ₁u(1-u), 0=Δv+w-v, w_t=Δw+▽·(w▽z)+μ₂w(1-w), 0=Δz-z+u, in bounded domain Ω⊂R^N, N≥1, subject to the homogeneous Neumann boundary conditions, and μ₁,μ₂>0. It is proved that for any nonegative initial data u₀(x),w₀(x)∈C(Ω), the solution (u(·,t),v(·,t),w(·,t),z(·,t)) is globally bounded. Furthermore, if μ₁,μ₂>(1)/(16), then (u(·,t),v(·,t),w(·,t),z(·,t)) converges asymptotically to the constant equilibrium (1,1,1,1) in the L^∞-norm as t→∞.

Key words: Attraction-repulsion, Chemotaxis, Logistic source, Boundedness, Asymptotic behavior

中图分类号:

O175.29

郜欣春, 周健, 田苗青. 带有Logistic源的吸引-排斥趋化性系统的整体有界性和渐近行为[J]. 数学物理学报, 2017, 37(1): 113-121.

Gao Xinchun, Zhou Jian, Tian Miaoqing. Global Boundedness and Asymptotic Behavior in an Attraction-Repulsion Chemotaxis System with Logistic Source[J]. Acta mathematica scientia,Series A, 2017, 37(1): 113-121.

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