项目名称: 吸引排斥趋化性模型的数学研究
项目编号: No.11501218
项目类型: 青年科学基金项目
立项/批准年度: 2016
项目学科: 数理科学和化学
项目作者: 金海洋
作者单位: 华南理工大学
项目金额: 18万元
中文摘要: 趋化性指的是细胞沿着化学物质梯度方向的运动。自从 Keller 和 Segel 在二十世纪七十年代提出趋化性的数学模型后,许多关于趋化性模型的数学研究相继展开。本项目研究的是于2003年由生物数学家提出的用于描述老年痴呆症患者中枢神经系统小神经胶质细胞聚集过程的吸引排斥趋化性模型。本项目拟对吸引排斥趋化性模型中吸引和排斥的竞争效应做深入和系统的数学研究,从而为进一步发展模型奠定理论基础。本项目主要有如下两个目标:(1) 改进已存在的关于解的全局动态行为的结果;(2)进一步发展模型,弥补原有模型存在的不足。
中文关键词: 趋化性;吸引排斥;整体解;爆破问题;临界质量
英文摘要: Chemotaxis describes the movement of cells in the direction of the chemical concentration gradient. The prototype of chemotaxis models was proposed by Kellel and Segel in 1970s, which has increasingly triggered a tremendous amount of works since then. In this project, we shall consider an attraction-repulsions Keller-Segel (ARKS) model proposed in 2003 to describe the aggregation of microglia cells formed in the central nervous system in Alzheimer’s disease. In this project, we will undertake more comprehensive and substantial analysis into this model to gain better understanding of the competing effects between the attraction and repulsion, and shed light on the further development of more realistic model. The main purposes of this project consists of two components: (1) Improvement of the existing analytical results on the global dynamics of solutions of the ARKS model; (2) Amendment of the ARKS model to fill the existing gap.
英文关键词: chemotaxis;attraction-repulsion;global solution;blow-up problem;critical mass