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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Ufimsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






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


Ufimsk. Mat. Zh., 2019, Volume 11, Issue 2, Pages 72–82 (Mi ufa472)  

Dirichlet boundary value problem for Aller–Lykov moisture transfer equation with fractional derivative in time

S. Kh. Gekkievaa, M. A. Kerefovb

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

Abstract: The heat-moisture transfer in soils is a fundamental base in addressing many problems of hydrology, agrophysics, building physics and other fields of science. The researchers focus on possibility of reflecting specific features of the studied arrays in the equations as well as their structure, physical properties, the processes going on in them, etc. In view of this, there arises a new class of fractional differential equations of state and transport being the base for most mathematical models describing a wide class of physical and chemical processes in media with a fractal structure and memory.
This paper studies the Dirichlet boundary value problem for the Aller–Lykov moisture transfer equation with the Riemann–Liouville fractional derivative in time. The considered equation is a generalization of the Aller-Lykov equation obtained by means of introducing the concept of the fractal rate of humidity change, which accounts the presence of flows moving against the moisture potential.
The existence of the solution to the Dirichlet boundary value problem is proved by the Fourier method. By means of energy inequalities method, for the solution we obtain an apriori estimate in terms of fractional Riemann-Liouville derivative, which implies the uniqueness of the solution.

Keywords: Aller–Lykov moisture transfer equation, Riemann–Liouville fractional derivative, Fourier method, apriori estimate.

Full text: PDF file (409 kB)
References: PDF file   HTML file

English version:
Ufa Mathematical Journal, 2019, 11:2, 71–81 (PDF, 346 kB); https://doi.org/10.13108/2019-11-2-71

Bibliographic databases:

UDC: 517.95
MSC: 35E99
Received: 20.02.2018

Citation: S. Kh. Gekkieva, M. A. Kerefov, “Dirichlet boundary value problem for Aller–Lykov moisture transfer equation with fractional derivative in time”, Ufimsk. Mat. Zh., 11:2 (2019), 72–82; Ufa Math. J., 11:2 (2019), 71–81

Citation in format AMSBIB
\Bibitem{GekKer19}
\by S.~Kh.~Gekkieva, M.~A.~Kerefov
\paper Dirichlet boundary value problem for Aller--Lykov moisture transfer equation with fractional derivative in time
\jour Ufimsk. Mat. Zh.
\yr 2019
\vol 11
\issue 2
\pages 72--82
\mathnet{http://mi.mathnet.ru/ufa472}
\transl
\jour Ufa Math. J.
\yr 2019
\vol 11
\issue 2
\pages 71--81
\crossref{https://doi.org/10.13108/2019-11-2-71}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000511171600005}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85078659783}


Linking options:
  • http://mi.mathnet.ru/eng/ufa472
  • http://mi.mathnet.ru/eng/ufa/v11/i2/p72

    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
  • Уфимский математический журнал
    Number of views:
    This page:138
    Full text:63
    References:11

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