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, 2017, Volume 102, Issue 1, Pages 6–16
DOI: https://doi.org/10.4213/mzm11478
(Mi mzm11478)
 

This article is cited in 1 scientific paper (total in 1 paper)

On a Nonlinear Third-Order Equation

A. I. Aristov

Lomonosov Moscow State University
Full-text PDF (454 kB) Citations (1)
References:
Abstract: A nonclassical nonlinear third-order partial differential equation modeling nonstationary processes in a semiconductor medium is studied. Seven classes of exact solutions of this equation given as explicit, implicit, and quadrature formulas are constructed. It is shown that, among these solutions, there are some bounded globally with respect to time and some approaching infinity on finite time intervals. These results are of interest in view of the following property of initial boundary-value problems for the given equation. Here the method of energy estimates used in many papers to justify the boundedness or unboundedness of solutions does not provide sufficient conditions for the unboundedness of solutions on finite time intervals.
Keywords: nonlinear partial differential equations, blow-up of solutions, exact solutions.
Received: 05.12.2016
English version:
Mathematical Notes, 2017, Volume 102, Issue 1, Pages 3–11
DOI: https://doi.org/10.1134/S000143461707001X
Bibliographic databases:
Document Type: Article
UDC: 517.955.8
Language: Russian
Citation: A. I. Aristov, “On a Nonlinear Third-Order Equation”, Mat. Zametki, 102:1 (2017), 6–16; Math. Notes, 102:1 (2017), 3–11
Citation in format AMSBIB
\Bibitem{Ari17}
\by A.~I.~Aristov
\paper On a Nonlinear Third-Order Equation
\jour Mat. Zametki
\yr 2017
\vol 102
\issue 1
\pages 6--16
\mathnet{http://mi.mathnet.ru/mzm11478}
\crossref{https://doi.org/10.4213/mzm11478}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3670205}
\elib{https://elibrary.ru/item.asp?id=29437439}
\transl
\jour Math. Notes
\yr 2017
\vol 102
\issue 1
\pages 3--11
\crossref{https://doi.org/10.1134/S000143461707001X}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000413842800001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85032391591}
Linking options:
  • https://www.mathnet.ru/eng/mzm11478
  • https://doi.org/10.4213/mzm11478
  • https://www.mathnet.ru/eng/mzm/v102/i1/p6
  • This publication is cited in the following 1 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, 2024