一类具有一般logistic源的高维生物趋化模型整体解的有界性  

Global Boundedness of Classical Solutions to a High-dimensional Chemotaxis Model with Generalized Logistic Source

作　　者：张冬冬 汤建钢 ZHANG Dong-dong;TANG Jian-gang(Jiangsu Middle School in Huocheng County,Huocheng 835200,China;College of Mathematics and Statistics,Yili University,Yining 835000,China)

机构地区：[1]霍城县江苏中学,新疆霍城835200 [2]伊犁师范大学数学与统计分院,新疆伊宁83500

出　　处：《数学的实践与认识》2022年第8期179-185,共7页Mathematics in Practice and Theory

基　　金：新疆维吾尔自治区“十三五”重点学科(数学)开放课题(XJZDXK-M2017006)。

摘　　要：考虑一个具有一般logistic源的高维山地松甲虫的扩散和聚集趋化模型,模型由两个扩散反应方程和一个常微分方程构成.通过G-N不等式讨论模型中系数之间的关系,再利用能量估计的方法证明在非负初值和充分光滑的齐次Neumman边界的条件下,模型的整体解一致存在且有界.A chemotaxis model with generalized logistic source describes the diffusion and aggregation of the Mountain Pine Beetle(MPB).The model consists of two reaction-diffusion equations and an ordinary differential equation.Through the G-N inequality discuss the relationship between a few coefficients in the model and the method of energy estimation is shown that the model admits global solution for homogeneous Neumann boundary conditions and non-negative initial data,which excludes the possibility offinite-time blow-up.

关 键 词：趋化性 存在性 整体有界性 logistic源 

分 类 号：Q141[生物学—生态学] O175[生物学—普通生物学]