On Problems of Extremum and Estimates of Control Function for Parabolic Equation

IF 0.2 Q4 MATHEMATICS Moscow University Mathematics Bulletin Pub Date : 2024-05-13 DOI:10.3103/s0027132224700050
I. V. Astashova, D. A. Lashin, A. V. Filinovskiy
{"title":"On Problems of Extremum and Estimates of Control Function for Parabolic Equation","authors":"I. V. Astashova, D. A. Lashin, A. V. Filinovskiy","doi":"10.3103/s0027132224700050","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider an extremum problem associated with a mathematical model of the temperature control. It is based on a one-dimensional non-self-adjoint parabolic equation of general form. Determining the optimal control as a function minimizing the weighted quadratic functional, we prove the existence of a solution to the problem of the double minimum by control and weight functions. We also obtain upper estimates for the norm of the control function in terms of the value of the functional. These estimates are used to prove the existence of the minimizing function for unbounded sets of control functions.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":null,"pages":null},"PeriodicalIF":0.2000,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow University Mathematics Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s0027132224700050","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

We consider an extremum problem associated with a mathematical model of the temperature control. It is based on a one-dimensional non-self-adjoint parabolic equation of general form. Determining the optimal control as a function minimizing the weighted quadratic functional, we prove the existence of a solution to the problem of the double minimum by control and weight functions. We also obtain upper estimates for the norm of the control function in terms of the value of the functional. These estimates are used to prove the existence of the minimizing function for unbounded sets of control functions.

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
论抛物方程控制函数的极值和估计问题
摘要 我们考虑了一个与温度控制数学模型相关的极值问题。它基于一般形式的一维非自交抛物方程。将最优控制确定为加权二次函数的最小化函数,我们证明了控制函数和加权函数双重最小值问题解的存在性。我们还获得了以函数值为单位的控制函数规范的上估计值。这些估计值用于证明无界控制函数集的最小化函数的存在性。
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 去求助
来源期刊
CiteScore
0.60
自引率
25.00%
发文量
13
期刊介绍: Moscow University Mathematics Bulletin  is the journal of scientific publications reflecting the most important areas of mathematical studies at Lomonosov Moscow State University. The journal covers research in theory of functions, functional analysis, algebra, geometry, topology, ordinary and partial differential equations, probability theory, stochastic processes, mathematical statistics, optimal control, number theory, mathematical logic, theory of algorithms, discrete mathematics and computational mathematics.
期刊最新文献
Invariants of Systems Having a Small Number of Degrees of Freedom with Dissipation On the Sequences of Polynomials $$\boldsymbol{f}$$ with a Periodic Continued Fraction Expansion $$\sqrt{\boldsymbol{f}}$$ On the Basis Property of the System of Exponentials and Trigonometric Systems of Sine and Cosine Functions in Weighted Grand Lebesgue Spaces Phase States Aggregation of Random Walk on a Multidimensional Lattice On Problems of Extremum and Estimates of Control Function for Parabolic Equation
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1