[1]江成顺.反应扩散模型解的爆破与避免爆破[J].南京师范大学学报(自然科学版),2018,41(01):9.[doi:10.3969/j.issn.1001-4616.2018.01.003]
　Jiang Chengshun.Blow-up of Solutions and Avoidance of Blow-up forSome Reaction Diffusion Models[J].Journal of Nanjing Normal University(Natural Science Edition),2018,41(01):9.[doi:10.3969/j.issn.1001-4616.2018.01.003]
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反应扩散模型解的爆破与避免爆破()
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《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第41卷
期数:
2018年01期
页码:
9
栏目:
·数学·
出版日期:
2018-03-31

文章信息/Info

Title:
Blow-up of Solutions and Avoidance of Blow-up forSome Reaction Diffusion Models
文章编号:
1001-4616(2018)01-0009-08
作者:
江成顺
武汉学院信息及传播学院,湖北 武汉 430212
Author(s):
Jiang Chengshun
Information and Communication,Wuhan College,Wuhan 430212,China
关键词:
反应扩散模型; 解的爆破; 格林函数; Volterra积分; 移动媒质; 避免爆破
Keywords:
reaction diffusion models; blow-up of solutions; green function; Volterra integral; mobile media; avoidance of blow-up
分类号:
O175.26
DOI:
10.3969/j.issn.1001-4616.2018.01.003
文献标志码:
A
摘要:
一些动态实际应用模型,如某些反应扩散模型,在一定条件下,可能会出现解的Blow up(爆破)现象. 但若能得知某一时刻将会出现Blow up现象,往往有某些特殊的办法来避免解发生Blow up. 基于此,文中首先讨论了某些反应扩散模型的局部解的存在唯一性; 然后利用构造辅助问题的方法和将偏微分方程转化为Volterra积分方程的技巧,给出了利用格林函数表示的模型局部解的解析表达式,在此基础上论证了模型解的爆破点集的有关性质,最后研究了相应模型如何避免解发生Blow up现象.
Abstract:
The actual application of some dynamic models,such as some reaction diffusion models,under certain conditions,there may be solutions of Blow up phenomenon. But when that moment will appear Blow up phenomenon,often due to some special measures to avoid the occurrence of Blow up. In view of this,at first,the author discussed the existence and uniqueness of local solutions to the corresponding reaction diffusion models. Then by using the method of constructing auxiliary problem,and the partial differential equation being transformed into Volterra integral equation techniques,the local solution of the models is given by using Green function represents. And based on the analysis of expression,the paper discussed the properties of the set for the Blow-up solutions of the models. Finally,the paper studied how to avoid the occurrence of Blow up solutions for the corresponding models.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2017-03-12.
基金项目:湖北省科技厅自然科学计划项目(2016CDC243).
通讯联系人:江成顺,博士,教授,研究方向:信息与计算科学,物联网工程等. E-mail:csjiang2005@126.com
更新日期/Last Update: 2018-03-31