Keller-Segel趋化模型解的全局存在性和爆破时间的下界估计

李远飞

doi:10.21656/1000-0887.420109

Keller-Segel趋化模型解的全局存在性和爆破时间的下界估计

doi: 10.21656/1000-0887.420109

李远飞

广州华商学院数学与统计研究所，广州 511300

基金项目: 广东省普通高校创新团队项目(2020WCXTD008)

详细信息

作者简介:
李远飞(1982—)，男，特聘教授，博士(E-mail：liqfd@163.com)

中图分类号: O178
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- 被引次数: 0
出版历程
- 收稿日期: 2021-04-25
- 修回日期: 2021-07-08
- 刊出日期: 2022-07-15

Global Existence of Solutions and Lower Bound Estimate of Blow-Up Time for the Keller-Segel Chemotaxis Model

LI Yuanfei

Institute of Mathematics and Statistics, Guangzhou Huashang College, Guangzhou 511300, P.R.China

摘要

摘要:
考虑了一个描述趋化细胞迁移的宏观非线性Keller-Segel模型, 其中该模型的存在区域$\varOmega\subset\mathbb{R}^N(N\geqslant2)$是有界的凸区域。利用能量估计的方法得到了$\varOmega\subset\mathbb{R}^3$上解的全局存在性。如果方程中的参数满足一定约束条件，证明了当$N=3$和$N=2$时可能的爆破时间的下界。
- Keller-Segel模型 /
- 下界 /
- 爆破 /
- 能量估计
Abstract:
A macroscopic nonlinear Keller-Segel model for chemotactic cell migration was considered, where the existence region of the model is a bounded convex one on$\varOmega\subset\mathbb{R}^N(N\geqslant2)$. The global existence of the solution on $\varOmega\subset\mathbb{R}^3$ was obtained by means of the energy estimate method. The lower bound of the blow-up time was proved for $N=3 $ and $N=2$.
- Keller-Segel model /
- lower bound /
- blow-up /
- energy estimate

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参考文献(22)

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