期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
一类 Keller-Segel趋化模型解在高维空间RN (N≥3)的爆破问题
- （广东金融学院 金融数学与统计学院，广东 广州 510521）
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DOI：10.13763/j.cnki.jhebnu.nse.202201017
Blow-up Problems of a Class of Keller-Segel Chemotaxis Models in High-dimensional SpaceRN (N≥3)
摘要/Abstract
摘要：
Keller-Segel体系在数学生物学、理论物理和工程学等方面都具有广泛应用，是应用数学领域的研究热点问题之一.考虑宏观的非线性Keller-Segel趋化模型，利用能量方法，首先构造一个能量表达式，然后运用高维Soblev嵌入不等式和一些微分不等式技巧，推导出能量所满足的一阶微分不等式，最终通过求解该不等式，得到Keller-Segel趋化模型爆破时间的下界.将以往的结果由低维空间推广到高维空间.
Abstract：
The Keller-Segel system,which has a wide range of applications in mathematical biology,engineering,and theoretical physics,is one of the frontiers of the research in the field of applied mathematics.We consider a macroscopic nonlinear Keller-Segel convergence model and use energy methods in this paper.First,we create an expression of energy.Then we use the high-dimensional Sobolev embedding inequality and some basic differential inequality techniques to derive the first-order differential inequality that the energy satisfies.Finally,we obtain a lower bound on the outbreak time of the Keller-Segel convergence model by solving this inequality.This article can generalize the previous results from low-dimensional space to high-dimensional space.
关键词
参考文献 22
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