Geodesic
Nonlocal boundary-value problem for the generalized Аller–Lykov moisture transport equation
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 4 (2018), pp. 19-28 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The mathematical modeling of different process types, for example, particle diffusion in a turbulent plasma, the propagation of heat in a thin rod, moisture transfer in soil, problems in mathematical biology and control problems, entails solving nonlocal boundary value problems. The paper considers a nonlocal boundary-value problem for the Aller–Lykov moisture transfer equation with a Riemann–Liouville time fractional derivative. The equation under consideration is a generalization of the Aller–Lykov equation obtained by introducing the concept of the fractal rate of humidity change, which explains the presence of flows moving against the water potential. For the solution to the problem, an a priori estimate has been obtained by the method of energy inequalities in terms of the fractional Riemann–Liouville derivative, which implies the uniqueness of the solution.
Keywords: equation of moisture transfer, fractional Riemann–Liouville derivative, generalized Aller–Lykov equation, a priori estimate. 
@article{VKAM_2018_4_a1,
     author = {S. Kh. Gekkieva},
     title = {Nonlocal boundary-value problem for the generalized {{\CYRA}ller{\textendash}Lykov} moisture transport equation},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {19--28},
     year = {2018},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2018_4_a1/}
}
TY  - JOUR
AU  - S. Kh. Gekkieva
TI  - Nonlocal boundary-value problem for the generalized Аller–Lykov moisture transport equation
JO  - Vestnik KRAUNC. Fiziko-matematičeskie nauki
PY  - 2018
SP  - 19
EP  - 28
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VKAM_2018_4_a1/
LA  - ru
ID  - VKAM_2018_4_a1
ER  - 
%0 Journal Article
%A S. Kh. Gekkieva
%T Nonlocal boundary-value problem for the generalized Аller–Lykov moisture transport equation
%J Vestnik KRAUNC. Fiziko-matematičeskie nauki
%D 2018
%P 19-28
%N 4
%U http://geodesic.mathdoc.fr/item/VKAM_2018_4_a1/
%G ru
%F VKAM_2018_4_a1
S. Kh. Gekkieva. Nonlocal boundary-value problem for the generalized Аller–Lykov moisture transport equation. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 4 (2018), pp. 19-28. http://geodesic.mathdoc.fr/item/VKAM_2018_4_a1/

[1] Chudnovskij A. F., Teplofizika pochv, Nauka, M., 1976, 352 pp.

[2] Nakhushev A. M., Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003, 272 pp.

[3] Kerefov M. A., “Ob odnoj kraevoj zadache dlya modificirovannogo uravneniya vlagoperenosa s drobnoj po vremeni proizvodnoj”, Dokl. Adyg. (Cherkes.) Mezhdunar. akad. nauk, 4:1 (1999), 12–14

[4] Kerefov M. A., Gekkieva S. Kh., “Kraevye zadachi dlya modificirovannogo uravneniya vlagoperenosa s drobnoj po vremeni proizvodnoj v mnogomernoj oblasti”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya: Matematika. Fizika., 41:23 (220) (2015), 17–23

[5] Kerefov M. A., Gekkieva S. Kh., “Nelokal'naya kraevaya zadacha dlya obobshchennogo uravneniya vlagoperenosa”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2017, no. 2, 106–112 | Zbl

[6] Kulik V. YA., “Issledovanie dvizheniya pochvennoj vlagi s tochki zreniya invariantnosti otnositel'no nepreryvnyh grupp preobrazovanij”, Issledovanie processov obmena ehnergiej i veshchestvom v sisteme pochva-rastenie-vozduh, Nauka, L., 1972, 315 pp. | Zbl

[7] Lafisheva M. M., Kerefov M. A., Dyshekova R. V., “Raznostnye skhemy dlya uravneniya vlagoperenosa Allera – Lykova s nelokal'nym usloviem”, Vladikavkazskij matematicheskij zhurnal, 19:1 (2017), 50–58 | MR

[8] Gekkieva S. Kh., “Pervaya kraevaya zadach dlya uravneniya vlagoperenosa Allera – Lykova s drobnoj po vremeni proizvodnoj”, Ustojchivoe razvitie: problemy, koncepcii, modeli, Materialy Vserossijskoj konferencii s mezhdunarodnym uchastiem, 2017, 99–102

[9] Chudnovskij A. F., “Nekotorye korrektivy v postanovke i reshenii zadach teplo i vlagoperenosa v pochve”, Cb. trudov po agrofizike, 1969, 41–54

[10] Kerefov M. A., Kraevye zadachi dlya modificirovannogo uravneniya vlagoperenosa s drobnoj po vremeni proizvodnoj, Dis. ... kand. fiz.-mat. nauk, Nal'chik, 2000, 75 pp.

[11] Bazzaev A. K., Gutnova D. K, SHkhanukov-Lafishev M. H., “Lokal'no-odnomernaya skhema dlya parabolicheskogo uravneniya s nelokal'nym usloviem”, Zh. vychisl. matem. i matem. fiz., 52:6 (2012), 1048–1057 | Zbl

[12] Arhestova S. M., Shkhanukov-Lafishev M. H, “Raznostnye skhemy dlya uravneniya vlagoperenosa Allera–Lykova s nelokal'nym usloviem”, Izvestiya Kabardino-Balkarskogo nauchnogo centra RAN, 2012, no. 3, 7–16

[13] Gekkieva S. Kh., Kerefov M. A., “Kraevye zadachi dlya obobshchennogo uravneniya vlagoperenosa”, Vestnik KRAUNC. Fiziko-matematicheskie nauki, 2018, no. 1 (21), 21–32 | MR

[14] Kerefov M. A., Gekkieva S. Kh., “Pervaya kraevaya zadacha dlya neodnorodnogo nelokal'nogo volnovogo uravneniya”, Vestnik Buryatskogo gosudarstvennogo universiteta. Matematika, informatika, 2016, no. 4, 76–86 | MR

[15] Pskhu A. V., Uravneniya v chastnyh proizvodnyh drobnogo poryadka, Nauka, M., 2005, 199 pp.