Bounds for global solutions of a reaction diffusion system with the Robin boundary conditions

IF 0.7 Q3 MATHEMATICS, APPLIED
K. Kita, M. Otani
{"title":"Bounds for global solutions of a reaction diffusion system with the Robin boundary conditions","authors":"K. Kita, M. Otani","doi":"10.7153/dea-2019-11-09","DOIUrl":null,"url":null,"abstract":"In this paper, we consider the large-time behavior of solutions of a reaction diffusion system arising from a nuclear reactor model with the Robin boundary conditions, which consists of two real-valued unknown functions. In particular, we show that global solutions of this system are uniformly bounded in a suitable norm with respect to time. Since this system has no variational structure, we cannot apply the standard methods relying on the Lyapunov functional in order to obtain a priori estimates of global solutions. To cope with this difficulty, we make use of the weighted $L^1$ norm characterized by the first eigenfunction of Laplacian with the Robin boundary condition.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2018-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations & Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/dea-2019-11-09","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1

Abstract

In this paper, we consider the large-time behavior of solutions of a reaction diffusion system arising from a nuclear reactor model with the Robin boundary conditions, which consists of two real-valued unknown functions. In particular, we show that global solutions of this system are uniformly bounded in a suitable norm with respect to time. Since this system has no variational structure, we cannot apply the standard methods relying on the Lyapunov functional in order to obtain a priori estimates of global solutions. To cope with this difficulty, we make use of the weighted $L^1$ norm characterized by the first eigenfunction of Laplacian with the Robin boundary condition.
具有Robin边界条件的反应扩散系统整体解的界
本文考虑由两个实值未知函数组成的具有Robin边界条件的核反应堆模型反应扩散系统解的大时间行为。特别地,我们证明了该系统的整体解是关于时间的一个合适范数的一致有界的。由于该系统没有变分结构,我们不能应用依赖于Lyapunov泛函的标准方法来获得全局解的先验估计。为了解决这一困难,我们利用了具有Robin边界条件的拉普拉斯第一特征函数特征的加权L^1范数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
33
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信