RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestnik YuUrGU. Ser. Mat. Model. Progr.:
Year:
Volume:
Issue:
Page:
Find






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


Vestnik YuUrGU. Ser. Mat. Model. Progr., 2015, Volume 8, Issue 3, Pages 141–147 (Mi vyuru281)  

Mathematical Modelling

On the regularizability conditions of integral equations

L. D. Menikhes, V. V. Karachik

South Ural State University, Chelyabinsk, Russian Federation

Abstract: Solving of integral equations of the first kind is an ill-posed problem. It is known that all problems can be divided into three disjoint classes: correct problems, ill-posed regularizable problems and ill-posed not regularizable problems. Problems of the first class are so good that no regularization method for them is needed. Problems of the third class are so bad that no one regularization method is applicable to them. A natural application field of the regularization method is the problems from the second class. But how to know that a particular integral equation belongs to the second class rather than to the third class? For this purpose a large number of sufficient regularizability conditions were constructed. In this article one infinite series of sufficient conditions for regularizability of integral equations constructed with the help of duality theory of Banach spaces is investigated. This method of constructing of sufficient conditions proved to be effective in solving of ill-posed problems. It is proved that these conditions are not pairwise equivalent even if we are restricted by the equations with the smooth symmetric kernels.

Keywords: integral equations; regularizability; smooth symmetric kernels.

DOI: https://doi.org/10.14529/mmp150309

Full text: PDF file (445 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.948
MSC: 47A52
Received: 15.05.2015
Language:

Citation: L. D. Menikhes, V. V. Karachik, “On the regularizability conditions of integral equations”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:3 (2015), 141–147

Citation in format AMSBIB
\Bibitem{MenKar15}
\by L.~D.~Menikhes, V.~V.~Karachik
\paper On the regularizability conditions of integral equations
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2015
\vol 8
\issue 3
\pages 141--147
\mathnet{http://mi.mathnet.ru/vyuru281}
\crossref{https://doi.org/10.14529/mmp150309}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000422201600009}
\elib{https://elibrary.ru/item.asp?id=24078401}


Linking options:
  • http://mi.mathnet.ru/eng/vyuru281
  • http://mi.mathnet.ru/eng/vyuru/v8/i3/p141

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:245
    Full text:94
    References:48

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020