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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
Year:
Volume:
Issue:
Page:
Find






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


Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2017, Volume 21, Number 1, Pages 80–93 (Mi vsgtu1495)  

Differential Equations and Mathematical Physics

The Dirichlet problem for a mixed-type equation with strong characteristic degeneracy and a singular coefficient

R. M. Safina

Volga Region State Academy of Physical Culture, Sport and Tourism, Kazan, 420010, Russian Federation

Abstract: In this paper we consider the first boundary value problem in a rectangular area for a mixed-type equation of the second kind with a singular coefficient. The criterion of the uniqueness of the problem solution is determined. The uniqueness of the problem solution is proved on the basis of completeness of the system of eigenfunctions of the corresponding one-dimensional spectral problem. The solution of the problem is built explicitly as a sum of Fourier–Bessel. There is the problem of the small denominators that appears when justifying the uniform convergence of the constructed series. In this regard, an evaluation of separateness from zero with a corresponding small denominator asymptotic behavior is found. This estimate has allowed to prove the convergence of the series and its derivatives up to the second order, and the existence theorem for the class of regular solutions of this equation.

Keywords: mixed-type equation, Dirichlet problem, singular coefficient, spectral method, uniqueness, Fourier–Bessel series, small denominators, existence

Funding Agency Grant Number
Russian Foundation for Basic Research 16-31-50008-мол_нр
This work was supported by the Russian Foundation for Basic Research (project no. 16–31–50008-mol_nr).


DOI: https://doi.org/10.14498/vsgtu1495

Full text: PDF file (652 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.956.6
Received: June 3, 2016
Revised: January 17, 2017
Accepted: March 13, 2017
First online: April 27, 2017

Citation: R. M. Safina, “The Dirichlet problem for a mixed-type equation with strong characteristic degeneracy and a singular coefficient”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:1 (2017), 80–93

Citation in format AMSBIB
\Bibitem{Saf17}
\by R.~M.~Safina
\paper The Dirichlet problem for a mixed-type equation
with strong characteristic degeneracy and a~singular coefficient
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2017
\vol 21
\issue 1
\pages 80--93
\mathnet{http://mi.mathnet.ru/vsgtu1495}
\crossref{https://doi.org/10.14498/vsgtu1495}
\elib{http://elibrary.ru/item.asp?id=29245098}


Linking options:
  • http://mi.mathnet.ru/eng/vsgtu1495
  • http://mi.mathnet.ru/eng/vsgtu/v221/i1/p80

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
    Number of views:
    This page:246
    Full text:89
    References:33

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020