Trudy Instituta Matematiki i Mekhaniki UrO RAN
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2019, Volume 25, Number 1, Pages 297–305
DOI: https://doi.org/10.21538/0134-4889-2019-25-1-297-305 (Mi timm1617) 		 
This article is cited in 9 scientific papers (total in 9 papers)

A control problem for a rod heating process with unknown temperature at the right end and unknown density of the heat source

V. I. Ukhobotov, I. V. Izmestyev

Chelyabinsk State University
Full-text PDF (183 kB) Citations (9)
References:
PDF
HTML
DOI: https://doi.org/10.21538/0134-4889-2019-25-1-297-305
Abstract: A control problem is considered for the process of heating a rod by varying the temperature at its left end. The exact values of the temperature at the right end of the rod and the heat density function are unknown; only the ranges of their possible values are given. The aim of the control is to ensure that the average temperature of the rod at a fixed time belongs to a given interval. We find necessary and sufficient conditions on the initial temperature of the rod under which the aim of the control can be achieved for any admissible unknown functions. The corresponding heating control at the left end of the rod is constructed.
Keywords: heat equation, temperature, control.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00264_а
This work was supported by the Russian Foundation for Basic Research (projects no. 18-01-00264_а).
Received: 10.12.2018
Revised: 28.12.2018
Accepted: 14.01.2019
Bibliographic databases:
Document Type: Article
UDC: 519.977
MSC: 49N70, 91A23
Language: Russian
Citation: V. I. Ukhobotov, I. V. Izmestyev, “A control problem for a rod heating process with unknown temperature at the right end and unknown density of the heat source”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 1, 2019, 297–305
Citation in format AMSBIB
\Bibitem{UkhIzm19}
\by V.~I.~Ukhobotov, I.~V.~Izmestyev
\paper A control problem for a rod heating process with unknown temperature at the right end and unknown density of the heat source
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2019
\vol 25
\issue 1
\pages 297--305
\mathnet{http://mi.mathnet.ru/timm1617}
\crossref{https://doi.org/10.21538/0134-4889-2019-25-1-297-305}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000470956900022}
\elib{https://elibrary.ru/item.asp?id=37051112}
Linking options:
  • https://www.mathnet.ru/eng/timm1617
  • https://www.mathnet.ru/eng/timm/v25/i1/p297
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Statistics & downloads:
    Abstract page:659
    Full-text PDF :200
    References:137
    First page:19
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2026