Email this article 
BOUNDARY VALUE PROBLEM FOR THE ALLER — LYKOV MOISTURE TRANSPORT GENERALIZED EQUATION WITH CONCENTRATED HEAT CAPACITY
- Authors: Kerefov M.A.1, Nakhusheva F.M.1, Gekkieva S.K.2
-
Affiliations:
- Kabardino-Balkarian State University named after H.M. Berbekov
- Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences
- Issue: Vol 24, No 3 (2018)
- Pages: 23-29
- Section: Articles
- URL: https://journals.ssau.ru/est/article/view/6449
- DOI: https://doi.org/10.18287/2541-7525-2018-24-3-23-29
- ID: 6449
Cite item
Full Text
Abstract
The article considers the Aller — Lykov equation with a Riemann — Liouville fractional time derivative, boundary conditions of the third kind and with the concentrated specific heat capacity on the boundary of the domain. Similar conditions arise in the case with a material of a higher thermal conductivity when solving a temperature problem for restricted environment with a heater as a concentrated heat capacity. Analogous conditions also arise in practices for regulating the water-salt regime of soils, when desalination of the upper layer is achieved by draining of a surface of the flooded for a while area. Using energy inequality methods, we obtained an a priori estimate in terms of the Riemann — Liouville fractional derivative, which revealed the uniqueness of the solution to the problem under consideration.
About the authors
M. A. Kerefov
Kabardino-Balkarian State University named after H.M. Berbekov
Author for correspondence.
Email: morenov@ssau.ru
F. M. Nakhusheva
Kabardino-Balkarian State University named after H.M. Berbekov
Email: morenov@ssau.ru
S. Kh. Gekkieva
Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences
Email: morenov@ssau.ru
References
- Barenblat G.I., Zheltov Yu.P., Kochina I.N. Ob osnovnykh predstavleniiakh teorii fil’tratsii odnorodnykh zhidkostei v treshchinovatykh porodakh . Prikladnaia matematika i mekhanika , 1960, Vol. 25, Issue 5, pp. 852–864 .
- Dzektser E.S. Uravneniia dvizheniia podzemnykh vod so svobodnoi poverkhnost’iu v mnogosloinykh sredakh . Dokl. AN SSSR , 1975, Vol. 220, no 3, pp. 540–543 .
- Rubinshtein L.I. K voprosu o protsesse rasprostraneniia tepla v geterogennykh sredakh . Izv. AN SSSR. Ser. geogr. , 1948, Vol. 12, no 1, pp. 27–45 .
- Ting T., Cooling A. Process according to two temperature theory of heat conduction. J. Math. Anal. Appl., 1974, Vol. 45, no 9, p. 23. DOI: http://doi.org/10.1016/0022-247X(74)90116-4 .
- Hallaire M. L’eau et la production vegetable. Institut National de la Recherche Agronomique, 1964, no 9 .
- Chudnovsky А.F. Teplofizika pochv . М.: Nauka, 1976, 352 p. .
- Nerpin S.V., Chudnovsky А.F. Energo- i massoobmen v sisteme rastenie-pochva-vozdukh . L.: Gidrometeoizdat, 1975, 358 p. .
- Nakhusheva F.M., Vodakhova V.А., Kudaeva F.Kh., Аbaeva Z.V. Lokal’no-odnomernaia skhema dlia uravneniia diffuzii drobnogo poriadka s sosredotochennoi teploemkost’iu . Sovremennye problemy nauki i obrazovaniia , 2015. no 2, p. 763. Available at: https://elibrary.ru/item.asp?id=24123596 .
- Nakhusheva F.M., Kudaeva F.Kh., Kaygermazov А.А., Karmokov M.M. Raznostnaia skhema dlia uravneniia diffuzii drobnogo poriadka s sosredotochennoi teploemkost’iu . Sovremennye problemy nauki i obrazovaniia
- , 2015, no 2, p. 839. Available at: https://elibrary.ru/item.asp?id=24921705
- .
- Shkhanukov-Lafishev M.Kh., Lafisheva M.M., Nakhusheva F.M., Mambetova А.B. Lokal’no-odnomernaia skhema dlia uravneniia teploprovodnosti s sosredotochennoi teploemkost’iu . Vladikavkazskii matem. zhurn. , 2013, Vol. 15, Issue 4, pp. 58–64. DOI: http://doi.org/10.23671/VNC.2013.4.7345 .
- Nakhushev A.M. Drobnoe ischislenie i ego primenenie . M.: Fizmatlit, 2003, 272 p. .
- Kulik V.Ya. Issledovanie dvizheniia pochvennoi vlagi s tochki zreniia invariantnosti otnositel’no nepreryvnykh grupp preobrazovanii . In: Sb. ”Issledovanie protsessov obmena energiei i veshchestvom v sisteme pochva-rastenie-vozdukh” . L.: Nauka, 1972 .
- Lafisheva M.M., Kerefov M.А., Dyshekova R.V. Raznostnye skhemy dlia uravneniia vlagoperenosa Allera — Lykova s nelokal’nym usloviem . Vladikavkazskii matem. zhurn. , 2017. Vol. 19, Issue 1, pp. 50–58. DOI: http://doi.org/10.23671/VNC.2017.1.5821 .
- Gekkieva S.Kh. Pervaia kraevaia zadach dlia uravneniia vlagoperenosa Allera — Lykova s drobnoi po vremeni proizvodnoi . Materialy Vserossiiskoi konferentsii s mezhdunarodnym uchastiem ”Ustoichivoe razvitie: problemy, kontseptsii, modeli” . Nalchik, 2017, pp. 99–102 .
- Аrkhestova S.M., Shkhanukov-Lafishev M.Kh. Raznostnye skhemy dlia uravneniia vlagoperenosa Allera — Lykova s nelokal’nym usloviem . Izvestiia Kabardino-Balkarskogo nauchnogo tsentra RAN , 2012, no 3 (47), pp. 7–16 .
- Gekkieva S.Kh., Kerefov M.А. Kraevye zadachi dlia obobshchennogo uravneniia vlagoperenosa . Vestnik KRAUNTs. Fiziko-matematicheskie
- nauki , 2018, no 1 (21), pp. 21–32. DOI: http://doi.org/10.18454/2079-6641-2018-21-1-21-31 .
- Pskhu А.V. Uravneniia v chastnykh proizvodnykh drobnogo poriadka . М.: Nauka, 2005, 199 p. .
- Ladyzhenskaya O. А. Kraevye zadachi matematicheskoi fiziki . М.: Nauka, 1973, 407 p. .
Supplementary files
