RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestnik KRAUNC. Fiz.-Mat. Nauki:
Year:
Volume:
Issue:
Page:
Find






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


Vestnik KRAUNC. Fiz.-Mat. Nauki, 2018, Issue 1, Pages 21–31 (Mi vkam230)  

MATHEMATICS

The boundary value problem for the generalized moisture transfer equation

S. Kh. Gekkievaa, M. A. Kerefovb

a Institute of Applied Mathematics and Automation of Kabardin-Balkar Scientific Center of RAS, 360000, Nalchik, Shortanova st., 89 A, Russia
b Kabardino-Balkarian State University named after H. M. Berbekov, 360004, Nalchik, Chernyshevsky st., 173, Russia

Abstract: In mathematical modeling of continuous media with memory, we deal with equations that describe a new type of wave motion, something between ordinary wave diffusion and classical wave propagation. There are fractional differential equations, which are the basis for the most mathematical models describing a wide class of physical and chemical processes in the fractal geometry of the Nature. The paper presents a new moisture transfer equation with a fractional Riemann–Liouville derivative that generalize the Aller–Lykov equation. The first boundary value problem for the generalized moisture transfer equation is considered. To prove the uniqueness of a solution we employ the energy inequalities method; an a priori estimate is obtained in terms of the fractional Riemann–Liouville derivative. The existence of the solution for the problem is proved by the Fourier method.

Keywords: Tricomi problem, parabolic-hyperbolic equation, non-characteristic plane, Fourier transform, maximum principle, apriori estimate, uniqueness, existence, system of integral equations.

DOI: https://doi.org/10.18454/2079-6641-2018-21-1-21-31

Full text: PDF file (237 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 517.95
MSC: 35E99
Received: 28.12.2017

Citation: S. Kh. Gekkieva, M. A. Kerefov, “The boundary value problem for the generalized moisture transfer equation”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2018, no. 1, 21–31

Citation in format AMSBIB
\Bibitem{GekKer18}
\by S.~Kh.~Gekkieva, M.~A.~Kerefov
\paper The boundary value problem for the generalized moisture transfer equation
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2018
\issue 1
\pages 21--31
\mathnet{http://mi.mathnet.ru/vkam230}
\crossref{https://doi.org/10.18454/2079-6641-2018-21-1-21-31}
\elib{http://elibrary.ru/item.asp?id=32833882}


Linking options:
  • http://mi.mathnet.ru/eng/vkam230
  • http://mi.mathnet.ru/eng/vkam/y2018/i1/p21

    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
  • Vestnik KRAUNC. Fiziko-Matematicheskie Nauki Vestnik KRAUNC. Fiziko-Matematicheskie Nauki
    Number of views:
    This page:18
    Full text:12

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018