Sbornik: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find




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

Sbornik: Mathematics, 2001, Volume 192, Issue 10, Pages 1417–1433
DOI: https://doi.org/10.1070/SM2001v192n10ABEH000599 (Mi sm599) 		 
This article is cited in 23 scientific papers (total in 24 papers)

From weak discontinuity to gradient catastrophe

S. V. Zakharov, A. M. Il'in

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
English version PDF (204 kB) Citations (24) Russian version article
References:
PDF
HTML
DOI: https://doi.org/10.1070/SM2001v192n10ABEH000599
Abstract: The Cauchy problem for a quasilinear parabolic equation with small parameter at the highest derivative is considered in the case when the solution of the degenerate equation has a weak discontinuity subsequently turning into a strong discontinuity. The singularities that the coefficients of the asymptotic formula representing the solution in the boundary layer of the weak discontinuity develop on approaching the point of the gradient catastrophe are analysed.
Received: 25.01.2001
Bibliographic databases:
UDC: 517.95
MSC: Primary 35B40, 35C20; Secondary 35K55
Language: English
Original paper language: Russian
Citation: S. V. Zakharov, A. M. Il'in, “From weak discontinuity to gradient catastrophe”, Sb. Math., 192:10 (2001), 1417–1433
Citation in format AMSBIB
\Bibitem{ZakIli01}
\by S.~V.~Zakharov, A.~M.~Il'in
\paper From weak discontinuity to gradient catastrophe
\jour Sb. Math.
\yr 2001
\vol 192
\issue 10
\pages 1417--1433
\mathnet{http://mi.mathnet.ru//eng/sm599}
\crossref{https://doi.org/10.1070/SM2001v192n10ABEH000599}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1867014}
\zmath{https://zbmath.org/?q=an:1028.35015}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000173373400008}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0035605741}
Linking options:
  • https://www.mathnet.ru/eng/sm599
  • https://doi.org/10.1070/SM2001v192n10ABEH000599
  • https://www.mathnet.ru/eng/sm/v192/i10/p3
    • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник - 1992–2005 Sbornik: Mathematics
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024