Contemporary Mathematics. Fundamental Directions
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Publishing Ethics

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


CMFD:
Year:
Volume:
Issue:
Page:
Find




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

Contemporary Mathematics. Fundamental Directions, 2013, Volume 47, Pages 60–77 (Mi cmfd223)  
This article is cited in 1 scientific paper (total in 1 paper)

Localized solutions of a piecewise linear model of the stationary Swift–Hohenberg equation on the line and on the plane

N. E. Kulagina, L. M. Lermanbc

a State University of Management, Moscow, Russia
b Research Institute for Applied Mathematics and Cybernetics, Lobachevski Nizhnii Novgorod State University, Nizhnii Novgorod, Russia
c Lobachevski Nizhni Novgorod State University, Faculty of Mechanics and Mathematics, Nizhni Novgorod, Russia
Full-text PDF (474 kB) Citations (1)
References:
PDF
HTML
Abstract: In this paper we study a simplified model of the stationary Swift–Hohenberg equation, where the cubic nonlinearity is replaced by a piecewise linear function with similar properties. The main goal is to prove the existence of so-called localized solutions of this equation, i.e., solutions decaying to a homogeneous zero state with unbounded increase of the space variable. The following two cases of the space variable are considered: one-dimensional (on the whole line) and two-dimensional; in the latter case, radially symmetric solutions are studied. The existence of such solutions and increase of their number with change in the equation parameters are shown.
English version:
Journal of Mathematical Sciences, 2014, Volume 202, Issue 5, Pages 684–702
DOI: https://doi.org/10.1007/s10958-014-2072-z
Bibliographic databases:
Document Type: Article
UDC: 517.925.41+517.956.25
Language: Russian
Citation: N. E. Kulagin, L. M. Lerman, “Localized solutions of a piecewise linear model of the stationary Swift–Hohenberg equation on the line and on the plane”, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 3, CMFD, 47, PFUR, M., 2013, 60–77; Journal of Mathematical Sciences, 202:5 (2014), 684–702
Citation in format AMSBIB
\Bibitem{KulLer13}
\by N.~E.~Kulagin, L.~M.~Lerman
\paper Localized solutions of a~piecewise linear model of the stationary Swift--Hohenberg equation on the line and on the plane
\inbook Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2011). Part~3
\serial CMFD
\yr 2013
\vol 47
\pages 60--77
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd223}
\transl
\jour Journal of Mathematical Sciences
\yr 2014
\vol 202
\issue 5
\pages 684--702
\crossref{https://doi.org/10.1007/s10958-014-2072-z}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84921935983}
Linking options:
  • https://www.mathnet.ru/eng/cmfd223
  • https://www.mathnet.ru/eng/cmfd/v47/p60
    • 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
    		Современная математика. Фундаментальные направления
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025