摘要
该文将研究如下问题■其中,有界区域Ω■R^(n)(1≦n≦5)具有光滑边界,v表示?Ω的外法向量,且0<γ(v)∈C^(3)[0,∞).在合适的初始条件下,该文分两种情形来研究模型的全局经典解的存在性与有界性:1<n<3;4≤n≤5,γ_(2)≥γ(v)≥γ_(1)>0,且|γ’(v)|≤γ_(3),v∈[0,∞),其中常数γ_(i)>0(i=1,2,3).接着,该文计算得到当t→∞时,其解(u,v,w,z)将指数收敛到平衡点■,其中■.
In this paper,we study the following problem■in a bounded domainΩ■R^(n)(1≦n≦5)with smooth boundary and v denotes the outward normal vector of■Ω,where 0<γ(v)∈C3[0,∞).Under suitably regular initial data,we show the existence of global classical solution with uniform-in-time bound under one of the following conditions●1<n<3,●4≤n≤5 andγ2≥γ(v)≥γ1>0,|γ’(v)l≤γ3,v∈[0,∞)with some constantsγi>0(i=1,2,3).Moreover,we confirm that the solution(u,v,w,z)will exponentially converge to the homogeneous equilibrium■as t→∞,where■0:=1/|Ω|∫Ωu0 dx,■0:=1/|Ω|∫Ωv0 dx and■0:=1/|Ω|∫Ωn w0 dx.
作者
史诗洁
刘正荣
赵晖
Shi Shijie;Liu Zhengrong;Zhao Hui(College of Big Data and Internet,Shenzhen Technology University,Guangdong Shenzhen 518118;School of Mathematics,South China University of Technology,Guangzhou 510640)
出处
《数学物理学报（A辑）》
CSCD
北大核心
2022年第2期502-519,共18页
Acta Mathematica Scientia
基金
国家自然科学基金(62172164,12026608,11971176,11901400)。
关键词
趋化模型
整体存在性
长时间行为
Chemotaxis model
Global existence
Large time behavior
