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.], 2016, Volume 20, Number 2, Pages 259–275 (Mi vsgtu1487)  

This article is cited in 2 scientific papers (total in 2 papers)

Differential Equations and Mathematical Physics

On one nonlocal problem for the Euler–Darboux equation

M. V. Dolgopolov, I. N. Rodionova, V. M. Dolgopolov

Samara National Research University, Samara, 443086, Russian Federation

Abstract: The boundary value problem with displacement is determined for the generalized Euler–Darboux equation in the field representing the first quadrant. This problem, unlike previous productions, specifies two conditions, connect integrals and fractional derivatives from the values of the sought solution in the boundary points. On the line of singularity of the coefficients of the equations the matching conditions continuous with respect to the solution and its normal derivation are considered. The authors took for the basis of solving the earlier obtained by themselves the Cauchy problem solution of the special class due to the integral representations of one of the specified functions acquired simple form both for positive and for negative values of Euler–Darboux equation parameter. The nonlocal problem set by the authors is reduced to the system of Volterra integral equations with unpacked operators, the only solution which is given explicitly in the corresponding class of functions. From the above the uniqueness of the solution of nonlocal problem follows. The existence is proved by the direct verification. This reasoning allowed us to obtain the solution of nonlocal problem in the explicit form both for the positive and for the negative values of Euler–Darboux equation parameter.

Keywords: integral equations system, boundary value problem, partial differential equation
Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1487

Full text: PDF file (870 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.956.3
MSC: 35L10, 35Q05
Original article submitted 20/III/2016
revision submitted – 18/V/2016

Citation: M. V. Dolgopolov, I. N. Rodionova, V. M. Dolgopolov, “On one nonlocal problem for the Euler–Darboux equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 20:2 (2016), 259–275

Citation in format AMSBIB
\Bibitem{DolRodDol16}
\by M.~V.~Dolgopolov, I.~N.~Rodionova, V.~M.~Dolgopolov
\paper On one nonlocal problem for the Euler--Darboux equation
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2016
\vol 20
\issue 2
\pages 259--275
\mathnet{http://mi.mathnet.ru/vsgtu1487}
\crossref{https://doi.org/10.14498/vsgtu1487}
\zmath{https://zbmath.org/?q=an:06964486}
\elib{https://elibrary.ru/item.asp?id=27126230}


Linking options:
  • http://mi.mathnet.ru/eng/vsgtu1487
  • http://mi.mathnet.ru/eng/vsgtu/v220/i2/p259

    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

    This publication is cited in the following articles:
    1. I. N. Rodionova, V. M. Dolgopolov, M. V. Dolgopolov, “Delta-problems for the generalized Euler–Darboux equation”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:3 (2017), 417–422  mathnet  crossref  zmath  elib
    2. M. V. Dolgopolov, I. N. Rodionova, “O postanovke vidoizmenennykh zadach dlya uravneniya Eilera–Darbu v sluchae parametrov, ravnykh po modulyu $\dfrac{1}{2}$”, Sovremennye problemy matematiki i fiziki, SMFN, 65, no. 1, Rossiiskii universitet druzhby narodov, M., 2019, 11–20  mathnet  crossref
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
    Number of views:
    This page:323
    Full text:97
    References:40
    First page:2

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