Matematicheskie Zametki
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. Zametki:
Year:
Volume:
Issue:
Page:
Find




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

Matematicheskie Zametki, 2011, Volume 89, Issue 3, Pages 393–409
DOI: https://doi.org/10.4213/mzm9048 (Mi mzm9048) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Weighted Identities for the Solutions of Generalized Korteweg–de Vries Equations

S. I. Pokhozhaev

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (506 kB) Citations (11)
References:
PDF
HTML
DOI: https://doi.org/10.4213/mzm9048
Abstract: Consider the Korteweg–de Vries equation $u_t+u_{xxx}+uu_{x}=0$ and its generalization $u_t+u_{xxx}+f(u)_{x}=0$. For the solutions of these equations, weighted identities (differential and integral) are obtained. These identities make it possible to establish the blow-up (in finite time) of the solutions of certain boundary-value problems.
Keywords: Korteweg–de Vries equation, initial boundary-value problem, weighted differential inequality, weighted integral inequality, blow-up of solutions, Hölder's inequality, Young's inequality, Dirichlet boundary condition.
Received: 08.09.2010
English version:
Mathematical Notes, 2011, Volume 89, Issue 3, Pages 382–396
DOI: https://doi.org/10.1134/S0001434611030102
Bibliographic databases:
Document Type: Article
UDC: 517.954
Language: Russian
Citation: S. I. Pokhozhaev, “Weighted Identities for the Solutions of Generalized Korteweg–de Vries Equations”, Mat. Zametki, 89:3 (2011), 393–409; Math. Notes, 89:3 (2011), 382–396
Citation in format AMSBIB
\Bibitem{Pok11}
\by S.~I.~Pokhozhaev
\paper Weighted Identities for the Solutions of Generalized Korteweg--de Vries Equations
\jour Mat. Zametki
\yr 2011
\vol 89
\issue 3
\pages 393--409
\mathnet{http://mi.mathnet.ru/mzm9048}
\crossref{https://doi.org/10.4213/mzm9048}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2856721}
\transl
\jour Math. Notes
\yr 2011
\vol 89
\issue 3
\pages 382--396
\crossref{https://doi.org/10.1134/S0001434611030102}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000290038700010}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79955639218}
Linking options:
  • https://www.mathnet.ru/eng/mzm9048
  • https://doi.org/10.4213/mzm9048
  • https://www.mathnet.ru/eng/mzm/v89/i3/p393
    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025