Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie
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 Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2020, Volume 13, Issue 2, Pages 17–32
DOI: https://doi.org/10.14529/mmp200202
(Mi vyuru540)
 

This article is cited in 5 scientific papers (total in 6 papers)

Mathematical Modelling

Positive solutions to Sobolev type equations with relatively $p$-sectorial operators

J. Banasiakab, N. A. Manakovaa, G. A. Sviridyuka

a South Ural State University, Chelyabinsk, Russian Federation
b University of Pretoria, Pretoria, South Africa
Full-text PDF (262 kB) Citations (6)
References:
Abstract: The article describes sufficient conditions for the existence of positive solutions to both the Cauchy problem and the Showalter–Sidorov problem for an abstract linear Sobolev type equation. A distinctive feature of such equations is the phenomenon of non-existence and non-uniqueness of solutions. The research is based on the theory of positive semigroups of operators and the theory of degenerate holomorphic semigroups of operators. The merger of these theories leads to a new theory of degenerate positive holomorphic semigroups of operators. In spaces of sequences, which are analogues of Sobolev function spaces, the constructed abstract theory is used to study a mathematical model. The results can be used to study economic and engineering problems.
Keywords: Sobolev type equations, positive degenerate holomorphic semigroups of operators, positive solution, Sobolev sequence spaces.
Received: 21.05.2019
Document Type: Article
UDC: 517.9
MSC: 43A35, 47B37
Language: English
Citation: J. Banasiak, N. A. Manakova, G. A. Sviridyuk, “Positive solutions to Sobolev type equations with relatively $p$-sectorial operators”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 13:2 (2020), 17–32
Citation in format AMSBIB
\Bibitem{BanManSvi20}
\by J.~Banasiak, N.~A.~Manakova, G.~A.~Sviridyuk
\paper Positive solutions to Sobolev type equations with relatively $p$-sectorial operators
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2020
\vol 13
\issue 2
\pages 17--32
\mathnet{http://mi.mathnet.ru/vyuru540}
\crossref{https://doi.org/10.14529/mmp200202}
Linking options:
  • https://www.mathnet.ru/eng/vyuru540
  • https://www.mathnet.ru/eng/vyuru/v13/i2/p17
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024