RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki:
Year:
Volume:
Issue:
Page:
Find






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


Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2018, Volume 28, Issue 1, Pages 82–90 (Mi vuu622)  

MATHEMATICS

Boundary value problem with shift for loaded hyperbolic-parabolic type equation involving fractional diffusion operator

K. U. Khubiev

Institute of Applied Mathematics and Automation, ul. Shortanova, 89 A, Nalchik, 360000, Russia

Abstract: The paper deals with non-local boundary-value problems with shift and discontinuous conjugation conditions in the line of type changing for a model loaded hyperbolic-parabolic type equation. The parabolic domain presents a fractional diffusion equation while the hyperbolic one presents a characteristically loaded wave equation. The uniqueness of the solution to the considered problems under certain conditions on the coefficients is proved by the Tricomi method. The existence of the solution involves solving the Fredholm integral equation of the second kind with respect to the trace of the sought solution in the line of type changing. The unique solvability of the integral equation implies the uniqueness of the solution to the problems. Once the integral equation is solved, the solution to the problems is reduced to solving the first boundary value problem for the fractional diffusion equation in the parabolic domain and the Cauchy problem for the inhomogeneous wave equation in the hyperbolic one. In addition, representation formulas are written out for solving the problems under study in the parabolic and hyperbolic domains.

Keywords: nonlocal problem, problem with shift, loaded equation, equation of mixed type, hyperbolic-parabolic type equation, fractional diffusion operator.

DOI: https://doi.org/10.20537/vm180108

Full text: PDF file (233 kB)
References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
UDC: 517.95
MSC: 35M10, 35M12
Received: 02.02.2018

Citation: K. U. Khubiev, “Boundary value problem with shift for loaded hyperbolic-parabolic type equation involving fractional diffusion operator”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:1 (2018), 82–90

Citation in format AMSBIB
\Bibitem{Khu18}
\by K.~U.~Khubiev
\paper Boundary value problem with shift for loaded hyperbolic-parabolic type equation involving fractional diffusion operator
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2018
\vol 28
\issue 1
\pages 82--90
\mathnet{http://mi.mathnet.ru/vuu622}
\crossref{https://doi.org/10.20537/vm180108}
\elib{http://elibrary.ru/item.asp?id=32697218}


Linking options:
  • http://mi.mathnet.ru/eng/vuu622
  • http://mi.mathnet.ru/eng/vuu/v28/i1/p82

    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 Удмуртского университета. Математика. Механика. Компьютерные науки
    Number of views:
    This page:126
    Full text:42
    References:19

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019