Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
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


Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find




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

Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 11, Pages 1850–1872
DOI: https://doi.org/10.31857/S0044466921110132 (Mi zvmmf11318) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Partial Differential Equations

Existence and stability of the solution to a system of two nonlinear diffusion equations in a medium with discontinuous characteristics

N. T. Levashova, B. V. Tischenko

Faculty of Physics, Lomonosov Moscow State University, 119991, Moscow, Russia
Citations (6)
DOI: https://doi.org/10.31857/S0044466921110132
Abstract: Asymptotic analysis is used to study the existence, local uniqueness, and asymptotic Lyapunov stability of the solution to a one-dimensional nonlinear parabolic system of the activator–inhibitor type. A specific feature of the problem is the discontinuities of the first kind of the functions on the right-hand sides of the equations. The jump of the functions occurs at a single point of the interval on which the problem is considered. The solution with a large gradient in the vicinity of the discontinuity is studied. The existence and stability theorems are proved using the asymptotic method of differential inequalities.
Key words: system of nonlinear equations, small parameter, inner layers, upper and lower solutions, asymptotics of solution, asymptotic Lyapunov stability.
Funding agency Grant number
Russian Science Foundation 18-11-00042П
This work was supported by the Russian Science Foundation, project no. 18-11-00042П.
Received: 23.12.2020
Revised: 24.03.2021
Accepted: 07.07.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 11, Pages 1811–1833
DOI: https://doi.org/10.1134/S0965542521110130
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: N. T. Levashova, B. V. Tischenko, “Existence and stability of the solution to a system of two nonlinear diffusion equations in a medium with discontinuous characteristics”, Zh. Vychisl. Mat. Mat. Fiz., 61:11 (2021), 1850–1872; Comput. Math. Math. Phys., 61:11 (2021), 1811–1833
Citation in format AMSBIB
\Bibitem{LevTis21}
\by N.~T.~Levashova, B.~V.~Tischenko
\paper Existence and stability of the solution to a system of two nonlinear diffusion equations in a medium with discontinuous characteristics
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2021
\vol 61
\issue 11
\pages 1850--1872
\mathnet{http://mi.mathnet.ru/zvmmf11318}
\crossref{https://doi.org/10.31857/S0044466921110132}
\elib{https://elibrary.ru/item.asp?id=46650245}
\transl
\jour Comput. Math. Math. Phys.
\yr 2021
\vol 61
\issue 11
\pages 1811--1833
\crossref{https://doi.org/10.1134/S0965542521110130}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000728906200008}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85120952690}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf11318
  • https://www.mathnet.ru/eng/zvmmf/v61/i11/p1850
    • 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
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Statistics & downloads:
    Abstract page:63
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024