具Logistic源的趋化模型在R^N中的全局经典解与渐近行为  

Global classical solutions and asymptotic behaviors in chemotaxis systems with Logistic source on R^N

作　　者：黄金凤 杜宛娟[1] HUANG Jinfeng;DU Wanjuan(School of Mathematics and Information,China West Normal University,Nanchong,Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《贵州师范大学学报（自然科学版）》2020年第5期45-49,98,共6页Journal of Guizhou Normal University：Natural Sciences

基　　金：四川省教育厅自然科学项目(14ZB0143);西华师大英才科研基金项目(17YC372)。

摘　　要：研究如下抛物-椭圆Keller-Segel趋化模型的柯西问题■,其中χ>0,a>0,b>0,k>1且N是正整数。首先,对于给定的初始函数u 0(x)=u(x,0;u 0),证明了该模型存在唯一的全局有界的经典解(u(x,t;u 0),v(x,t;u 0))。此外,对于某个常数C>0,参数满足a>max{2χC,2b·(2χ/kb)^k(k-1)},我们给出了解的渐近稳态解((a/b)^(1/k),a/b^(1/k))。This paper deals with the Cauchy problem of the parabolic-elliptic Keller-Segel chemotaxis model■,where the parametersχ,a,b are positive constants,k>1 and N is a positive integer.First,it is shown that this system possesses the global existence and boundedness of the classical solution(u(x,t;u 0),v(x,t;u 0))for the given initial function u 0(x)=u(x,0;u 0).Furthermore,we consider the asymptotic stability of the constant equilibrium((a/b)^(1/k),a/b^(1/k))for a>max{2χC,2b·(2χ/kb)^k(k-1)},with a constant C>0.

关 键 词：Keller-Segel模型 Logistc源项 全局经典解 渐近行为 

分 类 号：O175.2[理学—数学]